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 (z. t) of a 1D harmonic oscillator described initial wave function (1) (,0)= A[3(z) +4₁ (2)], where n in , is the quantum number. [1 point] Hints: (i) You can leave vo and implicit; (ii) Use the results obtained at points b) and c). e) Write the normalized expression of (x, t) constructed at point d). [3 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 (z. t) of a 1D harmonic oscillator described initial wave function (1) (,0)= A[3(z) +4₁ (2)], where n in , is the quantum number. [1 point] Hints: (i) You can leave vo and implicit; (ii) Use the results obtained at points b) and c). e) Write the normalized expression of (x, t) constructed at point d). [3 points]
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![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 wave
function
A[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]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa20122bf-410d-4a3b-97ef-dca9d41a62bd%2F011f58b1-4043-45f8-8645-068e4af051ab%2F3wokfb_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 wave
function
A[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]
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