2 The harmonic oscillator (7 points) ^)a) What is the expression of the Hamiltonian of the quantum 1D harmonic oscillator? [1 point]b) What is the ground state energy of the quantum harmonic oscillator? [1 point]c) What is the energy of the first excited state of the quantum harmonic oscillator? [1 point]d) Express the time-dependent wave function (a, t) of a 1D harmonic oscillator described initial wavefunctionA[3√(x) + 4(x)],(1)(a,0)where n in , is the quantum number. [1 point]Hints: (i) You can leave yo and implicit; (ii) Use the results obtained at points b) and c).e) Write the normalized expression of V(x, t) constructed at point d). [3 points]

(a) The expression for the Hamiltonian of the quantum 1D harmonic oscillator is given by:Where:(b)…

Answered: a) What is the expression of the…

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[QUANTUM MECHANICS - FINITE POTENTIAL BARRIER]
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