Quantum Mechanics-Spin-Statistics Connection (CSIR (Council of Scientific & Industrial Research) Physical Sciences): Questions 1 - 4 of 13

Question

In a basis in which the z – component of the spin is diagonal, an electron is in a spin state,

The probability that a measurement of will yield the value and are, respectively,

Question

A spin particle is in the state in the eigen basis and . If we measure , the probabilities of getting and , respectively, are (December)

Question

Consider a system of three spins S₁, S₂ and S₃ each of which can take values + 1 and –1. The energy of the system is given by , where J is a positive constant. The minimum energy and the corresponding number of spin configurations are, respectively – (December)

Question

A collection N of non – interacting spins , is kept in an external magnetic field B at a temperature T. The Hamiltonian of the system is . What should be the minimum value of for which the mean value ? (December)