How to understand the physics meanings for system x--> ix?

  • Thread starter dongsh2
  • Start date
  • #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?
 

Answers and Replies

  • #2
Demystifier
Science Advisor
Insights Author
10,690
3,414
For example, in Harmonic oscillator, we find E--> -E when x--> i x.
I don't think it is true, unless one also makes the transformation p->ip.
 
  • #3
27
0
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?
 
  • #4
9,332
2,321
A
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?
A mathematical quirk maybe - every mathematical idiosyncrasy doesn't necessarily have some deep meaning.

Thanks
Bill
 
  • #5
Demystifier
Science Advisor
Insights Author
10,690
3,414
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?
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?
 

Related Threads on How to understand the physics meanings for system x--> ix?

  • Last Post
Replies
5
Views
2K
Replies
3
Views
3K
Top