- #1

eljose79

- 214

- 1

Should you take all the possible permutation of it?..i have this problem...thanks.

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- Thread starter eljose79
- Start date

- #1

eljose79

- 214

- 1

Should you take all the possible permutation of it?..i have this problem...thanks.

- #2

Sonty

- 108

- 0

- #3

nbo10

- 418

- 5

hint. The Energy has to equal n*hbar

- #4

Originally posted by Sonty

^{m}*p^{n}symmetric.My first impulse would be to write it (x^{m}*p^{n}+ p^{n}*x^{m})/2, but I have strong doubts about it as I seem to have heared my teacher say "stick to those simple ones".

I don't see the point of expanding f(x). Here's what I'd do

H = [f(x)*P^n + P^n*f(x)]/2

Pete

- #5

Sonty

- 108

- 0

Originally posted by pmb

I don't see the point of expanding f(x).

Well, as a first thing I have to make sure H is a linear operator.

- #6

Of course it's linear. Regardless of what particular form it takes so long as it's a Hamiltonian I.e.Originally posted by Sonty

Well, as a first thing I have to make sure H is a linear operator.

H(a|Psi1> + b|Psi2>) = aH|Psi1> + bH|Psi2>

I.e. you take H and multiply it through. And example of a non-linear operator is O where O(A) = A^2

In the present case

H(Psi) = [f(x)P^n][a*Psi1 + b*Psi2]

= [f(x)P^n](a*Psi1) + [f(x)P^n](b*Psi2)

= a*[f(x)P^n]Psi1 + b*[f(x)P^n]Psi2

= a*H(Psi1) + b*H(Psi2)

However I don't see what possible physical system this Hamiltonian could belong to and thus the reason to call it a Hamiltonian. But that's par for the course sometimes. Goldstein's text has an example of a Hamiltonian in the problem section for which I can't see what physical system it describes either.

Pmb0

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