I have the state:
where [itex]\theta[/itex] is an arbitrary real number and [itex]|\psi>[/itex] is normalized.
And [itex]|0> and |1> refer to the ground state and first excited state of the harmonic oscillator.
Calculate the expectation value of the Hamiltonian for the harmonic oscillator.
The product of the raising and lowering operators
I also know that
The Attempt at a Solution
So far I know that I can solve this by converting the two states, 0 and 1, to the wave functions and solving the integral.
But I am curious as to how I can solve this using Dirac notation
specifically I cannot figure out how to apply the derivatives in the momentum operator from N using this notation.