The state of a particle moving in 1-D may be described by a density operator ρ. In the position representation, this will be described by a function ρ(x, x’). (a) What is the normalization condition...

The state of a particle moving in 1-D may be described by a density operator ρ. In the position representation, this will be described by a function ρ(x, x’).

(a) What is the normalization condition (Eq. 8.14) for ρ(x, x’)?

(b) Denote by |Gσ (p) the state described by a Gaussian wave packet with an envelope function φ(x) from Eq. 10.64 and a plane wave e^ikx
with hk = p. Find the position representation ρ(x, x’) for the density operator ρ =

(c) Suppose that the particle is in a mixture of Gaussian wave packet states with a continuous range of momenta near zero: