Quantum Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 53 - 59 of 80

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Question 53

Appeared in Year: 2007

Question

MCQ▾

There are only three bound states for a particle of mass in a one – dimensional potential well of the form shown in the figure. The depth of the potential satisfies –

A One Dimensional Potential Well

Choices

Choice (4)Response

a.

b.

c.

d.

Passage

An unperturbed two – level system has energy eigenvalues and , and eigenfunctions and . When perturbed, its Hamiltonian is represented by .

Question 54 (1 of 3 Based on Passage)

Appeared in Year: 2006

Question

MCQ▾

The first – order correction to the eigenfunction is –

Choices

Choice (4)Response

a.

b.

c.

d.

Question 55 (2 of 3 Based on Passage)

Appeared in Year: 2006

Question

MCQ▾

The second – order correction to is –

Choices

Choice (4)Response

a.

b.

0

c.

d.

Question 56 (3 of 3 Based on Passage)

Appeared in Year: 2006

Question

MCQ▾

The first – order correction to is –

Choices

Choice (4)Response

a.

A

b.

c.

d.

0

Question 57

Appeared in Year: 2007

Question

MCQ▾

The wavefunction of a particle, moving in a one dimensional time independent potential , is given by , where and are constants. This means that the potential is of the form,

Choices

Choice (4)Response

a.

b.

c.

d.

Question 58

Quantum Mechanics

Appeared in Year: 2008

Question

MCQ▾

Let denote the ground state of the hydrogen atom. Choose the correct statement from those given below –

Choices

Choice (4)Response

a.

b.

c.

d.

Passage

A particle of mass is confined in the ground state of a one – dimensional box, extending from to . The wavefunction of the particle in this state is , where is a constant.

Question 59 (1 of 3 Based on Passage)

Appeared in Year: 2007

Question

MCQ▾

The normalization factor of this wavefunction is –

Choices

Choice (4)Response

a.

b.

c.

d.

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