# GATE (Graduate Aptitude Test in Engineering) Physics: Questions 364 - 367 of 659

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## Question 364

Appeared in Year: *2009*

### Question

MCQ▾and represent two physical characteristics of a quantum system. If is Hermitian, then for the product to be Hermitian, it is sufficient that –

### Choices

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

a. | is Hermitian and and commute | |

b. | is Hermitian | |

c. | is anti – Hermitian | |

d. | is Hermitian and and anti – commute |

## Question 365

Appeared in Year: *2009*

### Question

MCQ▾The spin function of a free particle, in the basis in which is diagonal, can be written as and with eigenvalues and , respectively. In the given basis, the normalized eigen function of with eigenvalue –

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 366

Appeared in Year: *2009*

### Question

MCQ▾A particle is in the normalized state which is a superposition of the energy eigen states and . The average value of energy of the particle in the state is . The state is given by –

### Choices

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

b. | ||

c. | ||

d. |

## Question 367

Appeared in Year: *2009*

### Question

MCQ▾A classical particle is moving in an external potential field which is invariant under the following infinitesimal transformation –

Where is the matrix corresponding to rotation about the axis. The conserved quantities are (the symbols have their usual meaning)

### Choices

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

a. | ||

b. | ||

c. | ||

d. |