# Operator theory

1. Apr 12, 2007

### tpm

let be:

$$f( \hat H ) | \Psi > =0$$ where $$| \Psi >$$ is an 'Eigenvalue'

of the operator 'T' my question is if in this case the number

$$\hat T | \Psi > =E_{n} | \Psi >$$ satisfy $$f( E_{n}) =0$$

so the energies are precisely the roots of f(x).

2. Apr 13, 2007

### matt grime

|x> usually means an element in a Hilbert space, doesn't it, Jose? Why is that an 'Eigenvalue'. What is f. What is H? What is H-hat? What is T hat?

3. Apr 13, 2007

### AiRAVATA

I believe H is the Hamiltonian and T is the Kinetic Energy operators.

You may have better luck posting this in the Quantum Physics section.