True or False, explain your answer a) Wave functions of identical bosons are completely symmetrical under...

True or False, explain your answer

a) Wave functions of identical bosons are completely symmetrical under permutations

b) Particle A has mass m and particle B has mass 100m. Both have the same kinetic energy

E. They are incident on an infinitely long potential step of magnitude V where V > E.

Particle B has a smaller probability of getting reflected than particle A.

c) A massive spin-3/2 particle can decay into a particle of spin-0 and a particle of spin-1/2.

d) A massive spin-1 particle can decay into a particle of spin-0 and a particle of spin-1/2.

e) The radial wave function of a hydrogen energy eigenstate with non-zero orbital angular momentum vanishes at the origin.

Solutions

Expert Solution

a) True.

Wave function of identical bosons are completely symmetrical under permutations. The wave function is shown below and symmetrical with exchange of index 1 and 2.

b) False.

The reflection coefficient is independent of the mass of the particle. It only depends on the energy of the particle and barrier height

c) False.

For a particle decay, spin must be conserved. Here, it violates spin conservation.

d) False.

For a particle decay, spin must be conserved. Here, it violates spin conservation.

e) True.

At origin, orbital angular momentum is impossible to be defined as it becomes 0/0 form. Hence, the radial wave function vanishes for non-zero orbital angular momentum.

genius_generous answered 1 year ago

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