# Quantum Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 48 - 52 of 80

Access detailed explanations (illustrated with images and videos) to **659** questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. *Unlimited Access, Unlimited Time, on Unlimited Devices*!

View Sample Explanation or View Features.

Rs. 450.00 -OR-

How to register? Already Subscribed?

### Passage

A free particle of mass moves along the direction. At , the normalized wave function of the particle is given by , where is a real constant.

## Question 48 (2 of 2 Based on Passage)

Appeared in Year: *2009*

### Question

MCQ▾The expectation value of the particle energy is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 49

Appeared in Year: *2008*

### Question

MCQ▾For a physical system, two observables and are known to be compatible. Choose the correct implication from amongst those given below:

### Choices

Choice (4) | Response | |
---|---|---|

a. | Observation of and carried out on an arbitrary state of the physical system, lead to the identical results irrespective of the order in which the observations are made. | |

b. | Every non – degenerate eigenstate of must necessarily be an eigenstate of | |

c. | Every eigenstate of must necessarily be an eigenstate of | |

d. | When an observation of is carried out on an arbitrary state of the physical system, a subsequent observation of , leads to an unambiguous result |

## Question 50

Appeared in Year: *2007*

### Question

MCQ▾If , the value of is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 51

Appeared in Year: *2007*

### Question

MCQ▾An atomic state of hydrogen is represented by the following wavefunction:

Where is a constant. The quantum number of the state are –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 52

Appeared in Year: *2008*

### Question

MCQ▾A finite wave train, of an unspecified nature, propagates along the positive axis with a constant speed and without any change of shape. The differential equation among the four listed below, whose solution it must be, is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |