Quantum Mechanics-Variational Method (CSIR Physical Sciences): Questions 5 - 7 of 10

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Question number: 5

» Quantum Mechanics » Variational Method

Appeared in Year: 2013

MCQ▾

Question

The bound on the ground state energy of the Hamiltonian with an attractive delta – function potential, namely H=22md2dx2αδ(x)

Using the variational principle with the trial wavefunction ψ(x)=Aexp(bx2) is – [Given:0ettadt=Γ(a+1)] (June)

Choices

Choice (4) Response

a.

mα24π2

b.

mα25π2

c.

mα22π2

d.

mα2π2

Question number: 6

» Quantum Mechanics » Variational Method

Appeared in Year: 2012

MCQ▾

Question

What would be the ground state energy of the Hamiltonian – H=22md2dx2αδ(x) If variational principle is used to estimate it with the trial wavefunction ψ(x)=Aebx2 with b, as the variational parameter?

(Hint:x2ne2bx2dx=(2b)n12Γ(n+12)) (December)

Choices

Choice (4) Response

a.

α2mπ2

b.

mα2π2

c.

mα222

d.

2mα2π2

Question number: 7

» Quantum Mechanics » Variational Method

Appeared in Year: 2012

MCQ▾

Question

A variational calculation is done with the normalized trial wavefunction ψ(x)=154a52(a2x2) for the one dimensional potential well V(x)={0,if x a,if x >a , the ground state energy is estimated to be, (June)

Choices

Choice (4) Response

a.

322ma2

b.

524ma2

c.

533ma2

d.

325ma2

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