- #1

LarryS

Gold Member

- 319

- 20

*for it. Please help.*

**expression**Thanks in advance.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter LarryS
- Start date

- #1

LarryS

Gold Member

- 319

- 20

Thanks in advance.

- #2

DrClaude

Mentor

- 7,758

- 4,268

- #3

jtbell

Mentor

- 15,866

- 4,460

Are you referring to the animated graphs which have the real and imaginary parts in different colors? I’m pretty sure they’re just the real solutions of the time-independent SE, multiplied by the complex time-dependent phase factor: $$e^{-iEt/\hbar} = \cos (Et/\hbar) - i \sin(Et/\hbar)$$The Wikipedia entry for the QHO shows a graph for the imaginary part but nofor it.expression

- #4

George Jones

Staff Emeritus

Science Advisor

Gold Member

- 7,539

- 1,354

I have seen a few online lectures on solving the Schrodinger equation for the Quantum Harmonic Oscillator. The various solutions are products of the real-valued Gaussian function and the real-valued Hermite Polynomials. But I have never seen a mathematical expression for the imaginary part of those solutions. The Wikipedia entry for the QHO shows a graph for the imaginary part but nofor it.expression

Are you referring to the animated graphs which have the real and imaginary parts in different colors? I’m pretty sure they’re just the real solutions of the time-independent SE, multiplied by the complex time-dependent phase factor: $$e^{-iEt/\hbar} = \cos (Et/\hbar) - i \sin(Et/\hbar)$$

The first four real/imaginary animations are examples of this, but the last two animations are superpositions of time-dependent stationary states, i.e., as my first quantum instructor would say, "There is (spatial) sloshing."

- #5

- 20,129

- 10,868

Well, that may well be true, but it doesn't have to do anything with the classical counterparts plotted as A and B. The only state referring to this classical case is a coherent state (depicted as plot H). It's of course misleading to show real and imaginary parts, which both are not observable. What's observable in a statistical sense, being position-probability distributions, are the modulus squares. Than it should be immediately clear that the energy eigenstates are stationary states, i.e., nothing is moving at all!Are you referring to the animated graphs which have the real and imaginary parts in different colors? I’m pretty sure they’re just the real solutions of the time-independent SE, multiplied by the complex time-dependent phase factor: $$e^{-iEt/\hbar} = \cos (Et/\hbar) - i \sin(Et/\hbar)$$

- #6

LarryS

Gold Member

- 319

- 20

Yes, I was referring to those animated graphs. Thanks for the clarification.Are you referring to the animated graphs which have the real and imaginary parts in different colors? I’m pretty sure they’re just the real solutions of the time-independent SE, multiplied by the complex time-dependent phase factor: $$e^{-iEt/\hbar} = \cos (Et/\hbar) - i \sin(Et/\hbar)$$

- #7

- 1,531

- 554

Here's a video about this:

Share: