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- #2

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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

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

- #4

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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

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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?

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

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