Psove that 7or Harmonicascillator, the HamiltonianCan be iwritten as方w2,

The Hamiltonian operator when operated on a wavefunction, we get the energy for a state of the wave…

Answered: Prove that or Harmonic ascillator, the…

Prove that or Harmonic ascillator, the Hamiltonian Can be written as Ĥ = trow (ât.ât!)

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Part b
Need full detailed answer.
Prove the following: if the Hamiltonian is independent of time, then ∆E doesn't change in time. Show work and be explicit to prove the statement.
The Hamiltonian matrix has been constructed using an orthonormal basis. (1 1 0V (1 0 1) A = (2 1 0 )+(0 2 2 \2 1 4 where H = Hº + V and cis a constant. 1 2 0/ b) Use time-independent perturbation theory to determine the eigenvalues with corrections up to second order.