How to Solve Quantum Mechanics Problems Using Commutation Relations

[kib97153]

http://ejokeimg.pchome.com.tw/see-post.html?Flow_No=30201&cat=47&rank="

I try using the commutation relation of the position operator and the Hamiltonian, but failed.

Thanks for your kindly help!

 

[kib97153]

By the way, I don't know how to show the pics directly, sorry about that.

 

[StatMechGuy]

Multiply the left hand side by the energy denominator. Insert the hamiltonian operator. The commutator trick should then work.

 

[kib97153]

Multiply the left hand side by the energy denominator. Insert the hamiltonian operator. The commutator trick should then work.

Thanks for your reply.^^ You mean like this?
But it's not the original equation. I know that the commutator of position and Hamiltonian is equal to velocity multiplies by
i and hbar(positive or negative sign added). But what I want to know is how to transform the position operator "itself" into the "velocity form" in the first pic I posted. Or my procedure is simply incorrect?

 

[kib97153]

Ooooooooooops, I got through it, thanks for you help!
You are right! No further questions at all...