Is the Radial Momentum Operator Hermitian?

[plarq]

Does anyone has proof of radial momentum operator as an Hermitian operator? Thanks.

 

[lbrits]

By the radial momentum operator you mean the momentum conjugate to $$r$$? Sandwich it between two wavefunctions, integrate by parts, and all should work out. Remember the integration measure contains a factor of $$r^2$$.

 

[denian]

I can assure you that the radial momentum operator is indeed a Hermitian operator. This can be proven mathematically using the definition of Hermitian operators, which states that the operator must be equal to its adjoint. In the case of the radial momentum operator, its adjoint is the complex conjugate of the operator, and it can be shown that the two are indeed equal.

Furthermore, the Hermiticity of the radial momentum operator is a fundamental property in quantum mechanics, as it guarantees that the eigenvalues of the operator are real numbers. This is essential in interpreting and understanding the physical meaning of the operator and its associated measurements.

In summary, the radial momentum operator is a well-established and proven Hermitian operator, and there is ample evidence and mathematical proof to support this fact.