Name: 21 量子力学III (21. Quantum Mechanics III)
Uploaded: 2021-01-14T05:25:32.000Z
Duration: 1 h 15 min 47 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

I will tell you what we have done so far, and that's all you

really need to know, to follow what's going to

The first thing we learned is if you're studying a particle

living in one dimension, that's all I'm going to do the

whole time because it's mathematically easier and there

is not many new things you gain by going to higher dimensions.

There's a particle somewhere in this one-dimensional universe.

Everything you need to know about that particle is contained

in a function called the wave function, and is denoted by the

By the way, everything I'm doing now is called kinematics.

In other words, kinematics is a study of how to

describe a system completely at a given time.

For example, in classical mechanics for a

single particle the complete description of that particle is

Dynamics is the question of how this changes with time.

If you knew all you could know about the particle now can you

By predict the future we mean can you tell me what x

will be at a later time and p will be at a later

So the kinematics is just how much do you need to know at a

Once you've got x and p everything follows.

As I mentioned to you, the kinetic energy,

angular momentum is some cross product of position and

interest just by giving the position and momentum.

I claim now the equivalent of this pair of numbers in this

So it's a lot more information than you had in classical

In classical physics two numbers tell you the whole

Quantum theory says "give me a whole function",

and we all know a function is really infinite amount of

information because at every point x the function has a

height and you've got to give me all that.

you say it tells me everything I can know, well,

The first thing is that if you took the absolute square of this

function, that is the probability density to find it

By that I mean if you multiply both by some infinitesimal

Δx that is the probability that the particle

That means that you take this ψ and you square it.

So you will get something that will go to 0 here,

go up, go to zero, do something like that.

This is ψ^(2), and that's your probability

if the function p(x) has an area with the x-axis

like p(x)dx that's the actual probability that if you

look for this guy you'll find him or her or it in this

So we will make the requirement that the total probability to

It's up to you how you want to define probability.

You say, "What are the odds I will get through this

That doesn't add up to 1 that adds up to 100,

but it gives you the impression the relative odds are equal.

Jimmy the Greek may tell you something, 7 is to 4 something's

I mean, 7 divided by 11 is one thing and 4 divided by 11 is the

So in quantum theory the wave function you're given need not

necessarily have the property that its square integral is 1,

but you can rescale it by a suitable number,

I mean, if it's not 1, but if it's 100 then you divide

it by 10 and that function will have a square integral of 1.

That's the convention and it's a convenience,

and I will generally assume that we have done that.

And I also pointed out to you that the function ψ

and the function 3 times ψ stand for the same situation in

And if ψ is a water wave 3 inches versus

30 inches are not the same situation, they describe

But in quantum mechanics ψ and a multiple of ψ

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21 量子力学III (21. Quantum Mechanics III)

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