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

  1. Jan 20, 2015 #1
    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. jcsd
  3. Jan 20, 2015 #2


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    Science Advisor

    I don't think it is true, unless one also makes the transformation p->ip.
  4. Jan 20, 2015 #3
    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?
  5. Jan 20, 2015 #4


    Staff: Mentor

    A mathematical quirk maybe - every mathematical idiosyncrasy doesn't necessarily have some deep meaning.

  6. Jan 21, 2015 #5


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    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?
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