
English: 
This episode is sponsored by:
Hi guys!
Jade here.
So a few weeks ago, I made a video
on the Schrödinger equation.
And in it, I said that
...if we place an electron in a box,
...the probability that it could be found outside the box
...is zero.
And a lot of you commented with questions like,
"Oh, but what about quantum tunneling?"
"Isn't there some cases where the
electron can tunnel outside of the box?"
So I thought,
"What the heck, I'll just make a whole video about it."
It's super cool
...and I will answer that specific
question at the end of the video.
But first,
Well, the short version is in regular classical physics.
If you have a ball at the bottom of a hill,
...if it doesn't get a big enough push to get over the hill,
...it's kind of just stuck there.
Putting this into physics talk,
...if the ball doesn't have enough
...to get over the
...of the hill,
...it'll never get over,
...like,
...ever.
But of course, in quantum mechanics,
...things aren't so simple.
If we replace the ball with a quantum particle like an

English: 
This episode is sponsored by Brilliant.
Hi guys! Jade here. So a few weeks ago I
made a video on the Schrodinger equation
and in it I said that if we place an
electron in a box the probability that
it could be found outside the box is
zero, and a lot of you commented with
questions like "oh but what about quantum
tunneling? Isn't there some cases where
the electron can tunnel outside of the
box?", so I thought what the heck I'll just
make a whole video about it. It's super
cool and I will answer that specific
question at the end of the video, but
first, what is quantum tunneling? Well the
short version is in regular classical
physics if you have a ball at the bottom
of a hill, if it doesn't get a big enough
push to get over the hill it's kind of
just stuck there. Putting this into
physics talk, if the ball doesn't have
enough kinetic energy to get over the
potential energy of the hill, it'll never
get over, like, ever. But of course, in
quantum mechanics things aren't so
simple. If we replace the ball with a

English: 
...and the hill with some kind of
...even if the electron
...doesn't have enough kinetic energy
to jump the potential barrier,
...sometimes it can end up on the other side.
This is called:
And in this video, we're going to see how it works.
So now,
...the long version!
So one of the biggest differences
between quantum and classical physics
...is that quantum physics is probabilistic.
Unlike a ball,
...we can't pinpoint exactly where an electron is.
This comes from the
...which says that we can never know the exact
position and momentum of an object.
It's not because our measuring devices
are too crappy or because we're too slow,
...it's just something fundamental
about the laws of nature.
But not all hope is lost!
Maybe we don't know exactly where the electron is,
...but we know with a pretty high probability
that it's around here somewhere.
We can actually model these probabilities with a wave,
...or, more technically, a
This wavy cloud

English: 
quantum particle like an electron and
the hill with some kind of potential
barrier, even if the electron doesn't
have enough kinetic energy to jump the
potential barrier, sometimes it can end
up on the other side. This is called
quantum tunneling and in this video
we're going to see how it works. So now
the long version! So one of the biggest
differences between quantum and
classical physics is that quantum
physics is probabilistic. Unlike a ball
we can't pinpoint exactly where an
electron is. This comes from the
Heisenberg Uncertainty Principle which
says that we can never know the exact
position and momentum of an object. It's
not because our measuring devices are
too crappy or because we're too slow,
it's just something fundamental about
the laws of nature. But not all hope is
lost! Maybe we don't know exactly where
the electron is but we know with a
pretty high probability that it's around
here somewhere. We can actually model
these probabilities with a wave or, more

English: 
technically, a wave function. This wavy
cloud gives us the probabilities of
where the electron is likely to be, so
now instead of imagining a particle
traveling toward a barrier, imagine a
wave traveling toward a barrier.
Now when this wave collides with the
barrier, because the electron doesn't
have enough kinetic energy to make it
over, it gets reflected. But wait, what
about the whole tunneling thing? Well
there's this secret property of waves
you probably didn't learn in school.
Light is an electromagnetic wave so
let's imagine what happens when we shine
a light beam through glass. When we shine
a light beam through a piece of glass, at
the boundary where the glass meets the
air, the light beam will bend or refract.
You may have noticed this effect if
you've ever looked at a straw in your
water glass. The visual illusion comes
from the bending of light at the
boundary of two different mediums, in
this case, air and water. But refraction
isn't the only thing that can happen at
a boundary. Light can also get reflected.
The amount of light which is reflected

English: 
...gives us the probabilities of
where the electron is likely to be.
So now, instead of imagining a
particle traveling toward a barrier,
...imagine a wave traveling toward a barrier.
Now, when this wave collides with the barrier,
...because the electron doesn't have
enough kinetic energy to make it over,
...it gets reflected.
But wait.
Well, there's this secret property of waves
you probably didn't learn in school.
Light is an electromagnetic wave,
...so let's imagine what happens when
we shine a light beam through glass.
When we shine a light beam through a piece of glass,
...at the boundary where the glass meets the air,
...the light beam will bend or
You may have noticed this effect
...if you've ever looked at a straw in your water glass.
The visual illusion
...comes from the bending of light at
the boundary of two different mediums,
...in this case, air and water.
But refraction isn't the only thing
that can happen at a boundary.
Light can also get reflected.
The amount of light which is reflected and refracted

English: 
...depends on the angle that the light hits the boundary.
All mediums have a certain angle where
100% of the light beam is reflected.
This is called:
...and you may have heard that when this happens,
...100% of the INCIDENT beam goes
back as the REFLECTED beam.
But that's not true.
These are Maxwell's equations.
And though they may look innocent,
...they form the entire foundation
of classical electromagnetism.
Remember how we said that
...light is an electromagnetic wave?
This means that the way light
behaves in different scenarios
...can be predicted and modeled
by solving Maxwell's equations.
Now, when we solve these equations
for the case of total internal reflection,
...we get something very interesting.
This.
Isn't that interesting?
Instead of there being an abrupt drop-off
where the light hits the boundary,
...there's this very quick exponential drop-off.
This is shown by this term here:

English: 
and refracted depends on the angle that
the light hits the boundary. All mediums
have a certain angle where 100% of the
light beam is reflected. This is called
total internal reflection and you may
have heard that when this happens 100%
of the incident beam goes back into the
reflected beam, but that's not true.
These are Maxwell's equations and though
they may look innocent they form the
entire foundation of classical
electromagnetism. Remember how we said
that light is an electromagnetic wave?
This means that the way light behaves in
different scenarios can be predicted and
modeled by solving Maxwell's equations
now when we solve these equations for
the case of total internal reflection we
get something very interesting this
isn't that interesting instead of there
being an abrupt drop off where the light
hits the boundary there's this very
quick exponential drop off this is shown
by this term here I know this looks

English: 
I know this looks super complicated, and
...well,
...it is.
So let's just get rid of all that mumbo-jumbo here
...and just focus on the bit that matters.
This is a graph of e to the power 'x',
...which, as you see,
...models exponential growth.
But the term in our equation is
...e to the power of negative x,
...which is
...simply the backwards version of this
...exponential decay.
So we have this tiny little drop-off wave here.
This is called an
...which, in my opinion, is a very suitable name.
The word
...means:
An evanescent wave is pretty much
exactly what it sounds like.
It decays incredibly quickly,
...lasting only a few wavelengths before vanishing,
...so we can't usually see or detect it.
But,
...if we place another material sufficiently
close to the boundary of the first,
...sometimes the evanescent wave
...doesn't decay completely to zero
before hitting the next material.

English: 
super complicated and well it is so
let's just get rid of all that
mumbo-jumbo here and just focus on the
bit that matters this is a graph of e to
the power X which as you can see models
exponential growth but the term in our
equation is e to the power negative
which is simply the backwards version of
this exponential decay so we have this
tiny little drop off wave here this is
called an evanescent wave which in my
opinion is a very suitable name the word
evanescent means soon passing out of
sight memory or existence quickly fading
or disappearing an evanescent wave is
pretty much exactly what it sounds like
it decays incredibly quickly lasting
only a few wavelengths before vanishing
so we can't usually see or detect it but
if we place another material
sufficiently close to the boundary of
the first sometimes the evanescent wave
doesn't decay completely to zero before
hitting the next material so it can then

English: 
So it can then continue to travel onwards.
This is called:
And I recommend looking up
a demo on YouTube after this:
I would have shown you in this video,
...but for anyone who has read my Twitter bio,
...you know that experiments are not my forte.
I actually did try it,
...and it just... didn't work.
Time for a digression.
Optics was one of my favorite subjects in university,
...and we did a lot of work on evanescent waves.
But I never really got a physical intuition for why they're
...there.
The only answer I ever found is
..."because Maxwell's equations say so."
So, like, when you solve the equations,
...you end up with this decaying exponential.
But other than that, I can't really say a physical reason
...for why a wave can't just abruptly stop
at a boundary and change direction.
So if you do,
...please explain it to me in the comments.
Okay, digression over.
This wave might be puny,
...but it's the reason behind why
quantum tunneling is possible.
Remember that we're trading our
electron as a probability wave.
...which means that when it gets reflected here,

English: 
continue to travel onwards this is
called frustrated total internal
reflection and I recommend looking up a
demo on YouTube after this I would have
shown you in this video but for anyone
who has read my Twitter bio you know
that experiments are not my forte I
actually did try it and it just didn't
work my olds digression optics was one
of my favorite subjects in university
and we did a lot of work on evanescent
waves but I never really got a physical
intuition for why they're there the only
answer I ever found is because Maxwell's
equations say so like when you solve the
equations you end up with this decaying
exponential but other than that I can't
really say a physical reason for why a
wave can't just abruptly stop at a
boundary and change direction so if you
do please explain it to me in the
comments ok digression over this wave
might be puny but it's the reason behind
why quantum tunneling is possible
remember that we're trading our electron
as a probability wave which means that

English: 
when it gets reflected here in
evanescent wave forms at the boundary if
the barrier is thin enough sometimes
some of the wave actually makes it
through so if some of the wave makes it
through and this wave represents the
probability of the location of the
electrons then there's some very small
but nonzero probability that our
electron is over here even though this
probability is tiny because there are
usually so many quantum particles
involved in any physical process the
effects of Quan
tunneling a large enough to be essential
to nuclear fusion in stars spontaneous
mutation in DNA and scanning tunneling
microscopy it may seem stalling that
we're treating the wavefunction exactly
like an electromagnetic wave it's hard
to imagine something so abstract like
the probabilities of electron locations
as a real physical thing that travels
and reflects and tunnels the truth is
scientists still don't know exactly what
a wavefunction is they don't know
whether it's purely a mathematical tool
we've created to help us predict things

English: 
...an evanescent wave forms at the boundary.
If the barrier is thin enough,
...sometimes
...some of the wave actually makes it through.
So if some of the wave makes it through
...and THIS wave represents the probability
of the location of the electrons,
...then there's some very small but non-zero probability
...that our electron is over here,
...even though this probability is tiny.
Because there are usually so many quantum
particles involved in any physical process,
...the effects of quantum tunneling
are large enough to be essential to
...nuclear fusion in stars,
...spontaneous mutation in DNA, and
...scanning tunneling microscopy.
It may seem startling that we're treating the wave
function exactly like an electromagnetic wave.
It's hard to imagine something so abstract,
...like the probabilities of electron locations.
As a real physical thing that travels
and reflects and tunnels,
...the truth is scientists still don't know
exactly what the wave function is.
They don't know whether it's

English: 
...purely a mathematical tool we've created to
help us predict things about quantum objects
...or whether it's a real, physical wave.
But what they do know
...is that it can be modeled pretty much
perfectly by wave mechanics.
When we solve the Schrödinger wave equation
for the electron inside the barrier,
...we get this exponential decay,
...which is exactly what we would
expect of an evanescent wave.
Speaking of Schrödinger's equation,
...in my video about that I said:
If we place an electron in a box,
...the probability that it could be
found outside the box is zero.
And a lot of you are confused, because...
'What about tunneling?'
Well, the truth is
...I didn't specify this very well.
In a lot of university degrees,
...a particle in a box is the simplest case
we use to analyze Schrödinger's equation.
But, it's actually a particle in an infinite potential well.
So, instead of this being a box,
...look at it as a well with infinitely high and thick walls.
In tunneling, the barrier needs to be thin enough
...so that the evanescent wave
...doesn't have time to completely decay
to zero before reaching the other side.
Only then can it propagate onwards.

English: 
about quantum objects or whether it's a
real physical wave but what they do know
is that it can be modeled pretty much
perfectly by wave mechanics when we
solve the Schrodinger wave equation for
the electron inside the barrier we get
this exponential decay which is exactly
what we would expect of an evanescent
wave speaking of Schrodinger's equation
in my video about that I said if we
place an electron in a box the
probability that it could be found
outside the box is zero and a lot of you
are confused because what about
tunneling well the truth is I didn't
specify this very well in a lot of
university degrees a particle in a box
is the simplest case we use to analyze
Schrodinger's equation but it's actually
a particle in an infinite potential well
so instead of this being a box look at
it as a well with infinitely high and
thick walls in tunneling the barrier
needs to be thin enough so that the
evanescent wave doesn't have time to
completely decay to zero before reaching

English: 
the other side only then can it
propagate onwards with infinitely high
and thick walls that's obviously
impossible so yeah my bad didn't specify
infinity in my last video someone
commented asking whether it was futile
to try and truly understand quantum
mechanics without doing the math and my
immediate reaction was yes while you can
learn the catchphrases and get an
overall gist of what's going on to
really get that gut feeling of
understanding an intuition you need to
work through the problems and see what
the equations tell you I didn't really
understand the Schrodinger equation
until I solved it myself
brilliant org is a learning website with
an entire course dedicated to quantum
mechanics it starts with the very first
Berman's which reveals strange quantum
behavior and takes you all the way to
shredding equation it has this
interactive quiz style which I love
because you can work through problems at
your own pace and check your
understanding at every step
I actually just worked through these
quizzes on the mathematical foundations
of quantum physics and had a few of my

English: 
With infinitely high and thick walls,
...that's obviously impossible.
So yeah, my bad.
Didn't specify infinity.
In my last video,
...someone commented asking whether it was futile
...to try and truly understand quantum
mechanics without doing the math.
And my immediate reaction was:
Yes.
While you can learn the catchphrases and
get an overall gist of what's going on,
...to really get that gut feeling
of understanding the intuition,
...you need to work through the problems
and see what the equations tell you.
I didn't really understand the Schrödinger
equation until I solved it myself.
Brilliant.org is a learning website
...with an entire course dedicated
to quantum mechanics.
It starts with the very first experiments
which reveals strange quantum behavior,
...and takes you all the way to the Schrödinger equation.
It has this interactive quiz style, which I love,
...because you can work through
problems at your own pace
...and check your understanding at every step.
I actually just worked through these quizzes on the
mathematical foundations of quantum physics,
...and had a few of my own aha moments,

English: 
...as some questions I'd had since
university were finally answered.
There're also tons of other courses
...specialising in math, physics and computer science.
Brilliant is offering a 20% discount to the
first 200 people to sign up using this link.
Just go to:
...and start learning quantum physics today.
Thanks for watching, guys.
I hope you enjoyed the video.
It was actually the result of a poll I posted
on the YouTube Community tab.
And so, if you would like to be included in those polls
...and vote on your favorite topics,
...then just click the notification bell.
This video is also part of a quantum physics
series I've got going on at the moment,
...which I've linked for you at the end
of the video and in the description.
So, until next time.
Bye!

English: 
own aha moments as some questions I'd
had since University were finally
answered there are also tons of other
courses specialising in math physics and
computer science brilliant is offering a
20% discount to the first 200 people to
sign up using this link just go to
brilliant org slash up and Adam and
start learning quantum physics today
thanks for watching guys I hope you
enjoyed the video it was actually the
result of a poll I posted on the YouTube
community tab so if you would like to be
included in those polls and vote on your
favorite topics then just click the
notification bell this video is also
part of a quantum physics series I've
got going on at the moment which I've
linked for you at the end of the video
and in the description so until next
time bye
