# Quantum Mechanics-Harmonic Oscillator (GATE (Graduate Aptitude Test in Engineering) Physics): Questions 1 - 4 of 4

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 622 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 350.00 or

## Question number: 1

» Quantum Mechanics » Harmonic Oscillator

Appeared in Year: 2014

### Write in Short

A one dimensional harmonic oscillator is in the superposition of number states, , given by

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

## Passage

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

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

### Choices

Choice (4) Response

a.

b.

c.

d.

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

» Quantum Mechanics » Harmonic Oscillator

Appeared in Year: 2011

MCQ▾

### Question

The value of for which is orthogonal to is –

### Choices

Choice (4) Response

a.

1

b.

c.

2

d.

## Question number: 4

» Quantum Mechanics » Harmonic Oscillator

Appeared in Year: 2006

MCQ▾

### Question

A one – dimensional harmonic oscillation is in the state,

Where and 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.

c.

0

d.

f Page