Does H(r) Equal Hψ(r) in Quantum Mechanics?

[andyc100]

Does H(\underline{r})=H\psi(\underline{r}) ?

 

[andyc100]

...in my textbook it says that P\psi(\underline{r})=\psi(\underline{-r}) where P is the parity operator.

and that H(\underline{r})=H(\underline{-r})

Thus P\psi(\underline{r})=p\psi(\underline{r}) where p is the parity eigenvalue.

Im having difficulty getting to this myself. Could some one please show me how?

 

[dextercioby]

Does H(\underline{r})=H\psi(\underline{r}) ?

This makes no sense. In the lhs you have an operator and in the rhs you have a vector. Also, in you second post, the <conclusion> is actually an assumption. The assumption is that P is an operator in Hilbert space for which the spectral equation makes sense.