Quantum Mechanics-Angular Momentum and Spin (GATE Physics): Questions 1 - 4 of 7

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Question number: 1

» Quantum Mechanics » Angular Momentum and Spin

Appeared in Year: 2014

Short Answer Question▾

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A hydrogen atom is in the state ψ=821ψ20037ψ310+421ψ321

Where n,l,m in ψnlm denote the principal, orbital and magnetic quantum numbers, respectively. If L is the angular momentum operator, the average value of L2 is________ 2 .

Question number: 2

» 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

Question number: 3

» Quantum Mechanics » Angular Momentum and Spin

Appeared in Year: 2015

Short Answer Question▾

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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: 4

» Quantum Mechanics » Angular Momentum and Spin

Appeared in Year: 2014

Short Answer Question▾

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ψ1 and ψ2 are two orthogonal states of a spin 12 system. It is given that

ψ1=13(10)+23(01) Where (10) and (01) represent the spin – up and spin – down states, respectively. When the system is in the state ψ2 , its probability to be in the spin – up state is _ .

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