Calculate (xp) expectation value of Harmonic Oscillator using raising and lowering operators.
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- Find the expectation value of the energy of the state defined by Y = Po, where is an eigenstate of the one-dimensional harmonic oscillator (arbitrary v) and P is the reduced momentum operator, P = Px Applying the harmonic oscillator raising and lowering operatorsFor the quantum harmonic oscillator in one dimension, calculate the second-order energy disturbance and the first-order eigen-state for the perturbative potentials: (in the picture)The young and beautiful expert Hand written solution is not allowed
- Plot the first three wavefunctions and the first three energies for the particle in a box of length L and infinite potential outside the box. Do these for n = 1, n = 2, and n = 3Consider a weakly anharmonic a 1D oscillator with the poten- tial energy m U(x) = w?a² + Ba* 2 Calculate the energy levels in the first order in the small anharmonicity parameter 3 using TIPT and the ladder operators.Prove in the canonical ensemble that, as T ! 0, the microstate probability ℘m approaches a constant for any ground state m with lowest energy E0 but is otherwise zero for Em > E0 . What is the constant?