Quantum Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 6 - 12 of 80

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Question 6

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 7

Appeared in Year: 2016

Question

MCQ▾

are the Pauli matrices. The expression is equal to –

Choices

Choice (4)Response

a.

b.

c.

d.

Question 8

Quantum Mechanics

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 9

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 10

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 ________

Question 11

Appeared in Year: 2016

Question

MCQ▾

Which of the following operators is Hermitian?

Choices

Choice (4)Response

a.

b.

c.

d.

Question 12

Quantum Mechanics

Appeared in Year: 2015

Question

MCQ▾

Let L and p be the angular and linear momentum operates, respectively for a particle. The commutator gives –

Choices

Choice (4)Response

a.

b.

0

c.

d.

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