# Quantum Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 60 - 63 of 80

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### Passage

A particle of mass is confined in the ground state of a one – dimensional box, extending from to . The wavefunction of the particle in this state is , where is a constant.

## Question 60 (2 of 3 Based on Passage)

Quantum Mechanics

Appeared in Year: 2007

### Question

MCQ▾

The expectation value of ( is the momentum operator) in this state is –

### Choices

Choice (4)Response

a.

b.

c.

0

d.

## Question 61 (3 of 3 Based on Passage)

Appeared in Year: 2007

### Question

MCQ▾

The energy eigenvalue corresponding to this state is –

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 62

Appeared in Year: 2008

### Question

MCQ▾

A particle is placed in a one dimensional box of size along the axis . Which of the following is true?

### Choices

Choice (4)Response

a.

For an arbitrary state , the probability of finding the particle in the left half of the well is half

b.

In the ground state, the probability of finding the particle in the interval is half

c.

In the first excited state, the probability of finding the particle in the interval is half. This also holds for states with

d.

In the ground state, the particle has a definite momentum

## Question 63

Quantum Mechanics

Appeared in Year: 2008

### Question

MCQ▾

Consider the combined system of proton and electron in the hydrogen atom in its (electronic) ground state. Let denote the quantum number associated with the total angular momentum and let denote the magnitude of the expectation value of the net magnitude moment in the state. Which of the following pairs represents a possible state of the system ( is Bohr magneton) ?

### Choices

Choice (4)Response

a.

b.

c.

d.

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