Commutator of the Hamiltonian with Position and Hamiltonian with Momentum

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SUMMARY

The discussion focuses on the calculation of the commutators of the Hamiltonian with position and momentum operators in quantum mechanics. Specifically, the user encounters a factor of 2 in the denominator while computing the commutator of the Hamiltonian with position, which is expressed as \( \frac{p^2}{2m} \). Additionally, there is a request for assistance in proceeding with the commutator of the Hamiltonian with momentum, emphasizing the importance of applying these operators to a wavefunction from their common dense domain.

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arsenalfan
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To prove:

xnohou.gif

pnohou.gif


Commutator of the Hamiltonian with Position:
i have been trying to solve, but i am getting a factor of 2 in the denominator carried from p2/2m

Commutator of the Hamiltonian with Momentum:
i am not able to proceed at all...


Kindly help.. :(
 
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Please show us your work.
 
Post your work and take into consideration the hint to compute the commutators when applied on a wavefunction from their common dense everywhere domain.
 

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