Quantum Mechanics (GATE Physics): Questions 13 - 14 of 35

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Question number: 13

» Quantum Mechanics » Angular Momentum and Spin

Appeared in Year: 2015

Short Answer Question▾

Write in Short

Let the Hamiltonian for two spin 12 particles of equal masses m , momenta p1 and p2 and position r1 and r2 be

H=12mp12+12mp22+12mω2(r12+r22)+kσ1σ2

where σ1 and σ2 denote the corresponding Pauli matrices, ω=0.1eV and k=0.2eV . If the ground state has net spin zero, then the energy (in eV ) is ________.

Question number: 14

» 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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