Quantum Mechanics-Harmonic Oscillator (GATE Physics): Questions 1 - 4 of 4

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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, Equation , given by Equation

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

Passage

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

Equation

Equation , where Equation 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 Equation determined in above question, the expectation value of energy of the oscillator in the state Equation is –

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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

» Quantum Mechanics » Harmonic Oscillator

Appeared in Year: 2011

MCQ▾

Question

The value of Equation for which Equation is orthogonal to Equation is –

Choices

Choice (4) Response

a.

1

b.

Equation

c.

2

d.

Equation

Question number: 4

» Quantum Mechanics » Harmonic Oscillator

Appeared in Year: 2006

MCQ▾

Question

A one – dimensional harmonic oscillation is in the state,

Equation

Where Equation and Equation are the ground, first excited and second excited states, respectively. The probability of finding the oscillator in the ground state is –

Choices

Choice (4) Response

a.

1

b.

Equation

c.

0

d.

Equation

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