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b. (10 points) Explain what is the difference between the classical harmonic oscillator and the quantum harmonic oscillator in terms of their energy scheme (discrete or continuous). (Hint: you can draw the energy diagram of each oscillator and then you can use them for your explanation)? Explain the concept of quantization of energy using your own words? (Note: Your answer must be not less than five lines).
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Consider a one-dimensional simple harmonic oscillator whose classical angular frequency is ω0 . For t 0 there is also a time-dependent potential V(t)=F0 x cosω t where F0 is constant in both space and time. Obtain an expression for the expectation value ⟨x⟩as a function of time using time-dependent perturbation theory to lowest nonvanishing order. Is this procedure valid for ω≃ω0 ?[ You may use .⟨n^'|x| n⟩=√(ħ/ 2 m ω0)(√(n 1) δn^', n 1 √(n) δn^', n-1) .] | Numerade
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