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Part I: "A perturbed harmonic oscillator" a) Give at least one strong argument why the harmonic oscillator is such an important quantum system A 1-dimensional harmonic oscillator with Hamiltonian H = p^2/2m + 1/2m?_0^2x^2, is perturbed by a field given by H' = 1/2m?_0^2x^2 ? cos(?t). b) If ? = 0 (the field is constant in time) what would be the energy levels of the system? c) For ? ? 0, calculate the probability that the system will make a transition from state N to state M in time t, using first order perturbation theory, given that the system is initially prepared in state ?_N, or, in Dirac notation, |N?. Explain all your steps clearly. d) How can you maximize the transition amplitude? (give three options) 

          Part I: "A perturbed harmonic oscillator"

a) Give at least one strong argument why the harmonic oscillator is such an important quantum system

A 1-dimensional harmonic oscillator with Hamiltonian H = p^2/2m + 1/2m?_0^2x^2, is perturbed by a field given by H' = 1/2m?_0^2x^2 ? cos(?t).

b) If ? = 0 (the field is constant in time) what would be the energy levels of the system?

c) For ? ? 0, calculate the probability that the system will make a transition from state N to state M in time t, using first order perturbation theory, given that the system is initially prepared in state ?_N, or, in Dirac notation, |N?. Explain all your steps clearly.

d) How can you maximize the transition amplitude? (give three options)
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Part I: "A perturbed harmonic oscillator" a) Give at least one strong argument why the harmonic oscillator is such an important quantum system A 1-dimensional harmonic oscillator with Hamiltonian H = p^2/2m + 1/2m?0^2x^2, is perturbed by a field given by H' = 1/2m?0^2x^2 ? cos(?t). b) If ? = 0 (the field is constant in time) what would be the energy levels of the system? c) For ? ? 0, calculate the probability that the system will make a transition from state N to state M in time t, using first order perturbation theory, given that the system is initially prepared in state ?N, or, in Dirac notation, |N?. Explain all your steps clearly. d) How can you maximize the transition amplitude? (give three options)

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Part I: "A perturbed harmonic oscillator" a) Give at least one strong argument why the harmonic oscillator is such an important quantum system A 1-dimensional harmonic oscillator with Hamiltonian H = p^2/2m + 1/2mω_0^2x^2, is perturbed by a field given by H' = 1/2mω_0^2x^2 α cos(ωt). b) If ω = 0 (the field is constant in time) what would be the energy levels of the system? c) For ω ≠ 0, calculate the probability that the system will make a transition from state N to state M in time t, using first order perturbation theory, given that the system is initially prepared in state ψ_N, or, in Dirac notation, |N⟩. Explain all your steps clearly. d) How can you maximize the transition amplitude? (give three options)
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00:01 Here everyone, so here we have been given a mass which is a 60 kilogram and we have to accelerate it with the 1 .5 meter per second square in the upward direction.
00:14 So we required a force to do such thing.
00:18 So first of all, let's draw the free body diagram...
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