# GATE (Graduate Aptitude Test in Engineering) Physics: Questions 53 - 58 of 659

Access detailed explanations (illustrated with images and videos) to **659** questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. *Unlimited Access, Unlimited Time, on Unlimited Devices*!

View Sample Explanation or View Features.

Rs. 450.00 -OR-

How to register? Already Subscribed?

## Question 53

Appeared in Year: *2015*

### Question

MCQ▾In an inertial frame , two events A and B take place at and , respectively. The times at which these events take place in a frame moving with a velocity with respect to are given by –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 54

Appeared in Year: *2015*

### Write in Short

Short Answer▾The Pauli matrices for three spin particles are , respectively. The dimension of the Hilbert space required to define an operator is –

## Question 55

Appeared in Year: *2016*

### Question

MCQ▾are the Pauli matrices. The expression is equal to –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 56

Appeared in Year: *2014*

### Write in Short

Short Answer▾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 .

## Question 57

Appeared in Year: *2015*

### Question

MCQ▾An operator for a spin particle is given by , where denotes Pauli matrices and is a constant. The eigenvalue of are –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 58

Appeared in Year: *2015*

### Write in Short

Short Answer▾Consider a system of eight non – interacting, identical quantum particle of spin in a one dimensional box of length L. The minimum excitation energy of the system, in units of is ________