Quantum Mechanics-One, Two and Three-Dimensional Potential Problems (GATE Physics): Questions 1 - 3 of 19

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Question number: 1

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

Appeared in Year: 2015

MCQ▾

Question

The average energy U of a one dimensional quantum oscillator of frequency ω and in contact with a heat bath at temperature T is given by,

Choices

Choice (4) Response

a.

U=12ωcosh(12βω)

b.

U=12ωsinh(12βω)

c.

U=12ωtanh(12βω)

d.

U=12ωcoth(12βω)

Question number: 2

» 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: 3

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

Appeared in Year: 2014

MCQ▾

Question

The ground state and the first excited state wave function of a one dimensional infinite potential well are ψ1 and ψ2 , respectively. When two spin – up electrons are placed in this potential, which one of the following with x1 and x2 denoting the position of the two electrons, correctly represents the space part of the ground state wave function of the system?

Choices

Choice (4) Response

a.

12[ψ1(x1)ψ2(x2)ψ1(x2)ψ2(x1)]

b.

12[ψ1(x1)ψ2(x2)+ψ1(x2)ψ2(x1)]

c.

12[ψ1(x1)ψ2(x2)ψ1(x2)ψ2(x2)]

d.

12[ψ1(x1)ψ2(x1)+ψ1(x2)ψ2(x2)]

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