# 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 –

### Choices

Choice (4) | Response | |
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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 | |
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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 | |
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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 | |
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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 | |
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a. | ||

b. | ||

c. | ||

d. |

## Question 58

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 | |
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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 | |
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a. | ||

b. | ||

c. | ||

d. |