Quantum Mechanics-Harmonic Oscillator (GATE Physics): Questions 1 - 3 of 3

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Question number: 1

» Quantum Mechanics » Harmonic Oscillator

Appeared in Year: 2014

Short Answer Question▾

Write in Short

A one dimensional harmonic oscillator is in the superposition of number states, n , given by ψ=12 2+32 3.

The average energy of the oscillator in the given state is _ω .

Passage

In a one – dimensional harmonic oscillator, φ0,φ1 and φ2 are respectively the ground, first and the second excited states. These three states are normalized and are orthogonal to one another.

ψ1=φ02φ1+3φ2

ψ2=φ0φ1+αφ2 , where α is a constant.

Question number: 2 (1 of 2 Based on Passage) Show Passage

» Quantum Mechanics » Harmonic Oscillator

Appeared in Year: 2011

MCQ▾

Question

For the value of α determined in above question, the expectation value of energy of the oscillator in the state ψ2 is –

Choices

Choice (4) Response
a.

9ω2

b.

3ω2

c.

ω

d.

3ω

Question number: 3 (2 of 2 Based on Passage) Show Passage

» Quantum Mechanics » Harmonic Oscillator

Appeared in Year: 2011

MCQ▾

Question

The value of α for which ψ2 is orthogonal to ψ1 is –

Choices

Choice (4) Response
a.

1

b.

2

c.

2

d.

1

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