Particle in a box in momentum basis

In summary, the conversation discusses the difficulty in defining the momentum operator in an infinite potential box and the convenience of working in the position representation. The Hamiltonian operator is well-defined, but the momentum operator is not self-adjoint on the Hilbert space. The conversation also touches on the possibility of working in the momentum representation and the use of the lower and raising operator momentum equivalent.
  • #36
I will have to think and work it out. But essentially, as you say, the vectors in the domain of ##\hat{P}^\dagger## and ##\hat{P}## need not satisfy any extra boundary condition (save square integrability and vanishing at infinity), their domain should turn out same.
 
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  • #37
Ravi Mohan said:
I will have to think and work it out. But essentially, as you say, the vectors in the domain of ##\hat{P}^\dagger## and ##\hat{P}## need not satisfy any extra boundary condition (save square integrability and vanishing at infinity), their domain should turn out same.
Great, I think I got it! Thanks!
Also, your blog is excellent!
 

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