Quantum Mechanics (GATE Physics): Questions 8 - 12 of 77

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Question number: 8

» 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, n , given by ψ=12 2+32 3.

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

Question number: 9

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2015

MCQ▾

Question

An operator for a spin 12 particle is given by A^=λσB , where B=B2(x^+y^), σ denotes Pauli matrices and λ is a constant. The eigenvalue of A^ are –

Choices

Choice (4) Response

a.

0,λB

b.

±λB

c.

0,λB

d.

±λB2

Question number: 10

» Quantum Mechanics » Postulates of Quantum Mechanics

Appeared in Year: 2015

Short Answer Question▾

Write in Short

Consider a system of eight non – interacting, identical quantum particle of spin 32 in a one dimensional box of length L. The minimum excitation energy of the system, in units of π222mL2 is ________

Question number: 11

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2016

MCQ▾

Question

Which of the following operators is Hermitian?

Choices

Choice (4) Response

a.

id2dx2

b.

ddx

c.

d3dx3

d.

d2dx2

Question number: 12

» Quantum Mechanics » Angular Momentum and Spin

Appeared in Year: 2015

MCQ▾

Question

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

Choices

Choice (4) Response

a.

ipz

b.

0

c.

ipz

d.

ipx

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