GATE Physics: Questions 55 - 59 of 323

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Question number: 55

» Quantum Mechanics » One, Two and Three-Dimensional Potential Problems

Appeared in Year: 2015

Short Answer Question▾

Write in Short

The Pauli matrices for three spin 12 particles are σ1,σ2andσ3 , respectively. The dimension of the Hilbert space required to define an operator O^=σ1σ2×σ3 is –

Question number: 56

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2016

MCQ▾

Question

σx,σyandσz are the Pauli matrices. The expression 2σxσy+σyσx is equal to –

Choices

Choice (4) Response

a.

iσz

b.

3iσz

c.

3iσz

d.

iσz

Question number: 57

» 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: 58

» 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: 59

» 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 ________

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