Q0.
(a) Q 1. Find the condition at which de Broglie wavelength equals the Compton wavelength. de Broglie wavelength for a particle.
(b)
The time independent wave function of a system is ψ
(x) = A exp(i kx);
(i) Is this wave function normalizable in the domain -∞ < x < ∞? Calculate the probability current density for this function.
(ii) The components of arbitrary vectors 𝐀 and 𝐁 commute with those of σ.
(c) (σ·A)(σ·B) = A·B + i σ·(A × B).
(d) An atomic state is denoted by { }^{4}D_{5/2}. What should be the minimum number of electrons involved for this state? Give a possible electron configuration.
(e)
Often the intensity of rotational transition J = 0 → J = 1 is not the most intense. Explain.
(f) Evaluate the commutator [∂^2/∂x2, x] and hence show that [p2, x] = -2 i ħ p.