- #1

- 747

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Should I use the Hamiltonian operator here?

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- Thread starter Reshma
- Start date

- #1

- 747

- 4

Should I use the Hamiltonian operator here?

- #2

- 574

- 1

Yes. You should get something very similiar to the harmonic oscillator.

- #3

- 747

- 4

[tex]V(x) = {1\over 2} m \omega^2 x^2[/tex]

Comparing it with [itex]V(x) = x^2[/tex],

[tex]{1\over 2} m \omega^2 = 1[/tex]

[tex]\omega = \sqrt{2\over m}[/tex]

And I substitute this value in the formula:

[tex]E_n = \hbar \omega \left(n + {1\over 2}\right)[/tex]

Am I going right?

- #4

- 335

- 4

Reshma said:

[tex]V(x) = {1\over 2} m \omega^2 x^2[/tex]

Comparing it with [itex]V(x) = x^2[/tex],

[tex]{1\over 2} m \omega^2 = 1[/tex]

[tex]\omega = \sqrt{2\over m}[/tex]

And I substitute this value in the formula:

[tex]E_n = \hbar \omega \left(n + {1\over 2}\right)[/tex]

Am I going right?

It looks good (Of course, n=0 for the ground state, don't forget that!), but make sure you know how to do the problem from scratch. I'm guessing that's what your professor wanted you to do.

-Dan

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