GATE Physics: Questions 89 - 91 of 622

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Question number: 89

» Classical Mechanics » Lagrange's and Hamilton's Formalisms

Appeared in Year: 2014

MCQ▾

Question

The Hamilton’s canonical equations of motion in terms of Poisson Brackets are –

Choices

Choice (4) Response

a.

q˙={H,p};p˙={H.q}

b.

q˙={H,q};p˙={H,P}

c.

q˙={q,H};p˙={p.H}

d.

q˙={p,H};p˙={q,H}

Question number: 90

» 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)]

Question number: 91

» Quantum Mechanics » Angular Momentum and Spin

Appeared in Year: 2014

Short Answer Question▾

Write in Short

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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