- #1

bluestar

- 80

- 0

Can someone define the “i” ?

One source I am looking at is:

galileo.phys.virginia.edu/classes/252/electron_in_a_box "dot" html

It will be the first equation.

Thanks

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- Thread starter bluestar
- Start date

- #1

bluestar

- 80

- 0

Can someone define the “i” ?

One source I am looking at is:

galileo.phys.virginia.edu/classes/252/electron_in_a_box "dot" html

It will be the first equation.

Thanks

- #2

DavidWhitbeck

- 351

- 1

It's the imaginary number, [tex]i = \sqrt{-1}[/tex].

- #3

cesiumfrog

- 2,010

- 5

You might alternatively think of it as an operator that advances a wave by one quarter cycle.

Notice how wave-number (multiplied onto the wave-function) is exactly that far out of phase from spatial derivative (operated onto the wave-function)? This (which you should recognise as "the momentum operator") gives an example of why complex numbers are convenient when describing waves.

Notice how wave-number (multiplied onto the wave-function) is exactly that far out of phase from spatial derivative (operated onto the wave-function)? This (which you should recognise as "the momentum operator") gives an example of why complex numbers are convenient when describing waves.

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- #4

bluestar

- 80

- 0

Dang, I forgot about i = sqrt(-1)

I haven’t used that in years. …Thanks,

Very interesting comment CesiumFrog.

I’ll consider that as I proceed with my work.

- #5

kahoomann

- 58

- 1

You might alternatively think of it as an operator that advances a wave by one quarter cycle.

Notice how wave-number (multiplied onto the wave-function) is exactly that far out of phase from spatial derivative (operated onto the wave-function)? This (which you should recognise as "the momentum operator") gives an example of why complex numbers are convenient when describing waves.

But what does Schrodinger equation mean?

We know what Newton's equation (F=ma) means

- #6

jsc314159

- 21

- 0

Does that make sense or am I full of hot air?

jsc

- #7

bluestar

- 80

- 0

Great Question Kahoomann

I have been studying the Schrodinger equation and its various spinoffs and here is what I have learned. Remember I am the novice and I am sure the pros may ring-in on the subject.

1st DeBroglie made the connection that atomic and subatomic particles exhibit wave properties.

2nd Schrodinger felt there was a connection between the wave-particle duality and the energy of the particle. Schrodinger derived a formula that described the energy of the particle in terms of a wave equation. The energy of the particle was equal to two parts of the wave equation. The first part results from the kinetic energy of the particle and the second part is the influence of a external field that may have an effect on the particle.

3rd From Schrodinger’s equation several things can be described or predicted in the atomic and subatomic world.

- #8

Fredrik

Staff Emeritus

Science Advisor

Gold Member

- 10,875

- 421

I'll pretend that space is one-dimensional here, just to simplify the notation.But what does Schrodinger equation mean?

We know what Newton's equation (F=ma) means

What Newton's second law really says is that position as a function of time satisfies a differential equation that's nice enough to guarantee that there exists a unique solution for each initial condition. This means that we if we know the position and velocity at one time, we can calculate position as a function of time, and that function tells us the position and velocity at

What quantum mechanics tells us is that a state can't be represented by a pair of numbers (x

When you solve it, you find that the solutions are of the form exp(-iEt+ipx). This is an eigenfunction of id/dt with eigenvalue E, and an eigenfunction of -id/dx with eigenvalue p. The identification of this E and p with energy and momentum comes from the fact that if you substitute the energy and momentum in the classical non-relativistic equation E=p

So the Schrödinger equation can be thought of as the quantum version of E=p

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- #9

Mohandas

- 7

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While F=ma determines x(t) for all future time, the Schrödinger equation determines Psi(x,t) for all future time. So while Newtons F=ma returns x(t), the S.E returns a

At this point it is hard to see how this can represent a state of a particle, given the fact that particles are not spread out in space, but, rather, they are localized at some point. Enter Statistical Interpretation; all quantum mechanics has to offer (compared to F=ma) is

- #10

Fredrik

Staff Emeritus

Science Advisor

Gold Member

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This is just something we have to get used to when we learn quantum mechanics. Between measurements, physical systems can be in states that do

So the assumption that the spin component of an electron always has a definite value is definitely false. There's no reason to think position is any different. We just have to get used to the fact that in quantum mechanics, the answer to the question "where is the particle now?" isn't a number (or 3 numbers), it's a complex-valued function (which also happens to be the answer to many other questions we may want to ask about the particle, like "what's its momentum?").

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