- #1

- 27

- 0

## Main Question or Discussion Point

For example, in Harmonic oscillator, we find E--> -E when x--> i x. How to understand physical meanings or in mathematics? How to understand the wave function in this case?

- Thread starter dongsh2
- Start date

- #1

- 27

- 0

For example, in Harmonic oscillator, we find E--> -E when x--> i x. How to understand physical meanings or in mathematics? How to understand the wave function in this case?

- #2

Demystifier

Science Advisor

- 10,690

- 3,414

I don't think it is true, unless one also makes the transformation p->ip.For example, in Harmonic oscillator, we find E--> -E when x--> i x.

- #3

- 27

- 0

What is the reason why also p-->ip?

- #4

bhobba

Mentor

- 9,332

- 2,321

A mathematical quirk maybe - every mathematical idiosyncrasy doesn't necessarily have some deep meaning.In harmonic oscillator, if we take x--> ix, the energy becones E_n= -(n+1/2), the wave function is changed by replacing "ix". We can check the cases n=0,1, etc. we find they indeed satisfy the Schrödinger equation.What is the reason why also p-->ip?

Thanks

Bill

- #5

Demystifier

Science Advisor

- 10,690

- 3,414

How do you calculate energy when you take x->-x? Do you perhaps take the Hamiltonian to act on the wave function? If yes, does that Hamiltonian depend also on p?

What is the reason why also p-->ip?

- Last Post

- Replies
- 5

- Views
- 2K

- Replies
- 3

- Views
- 3K