Question

1. The wave-functions of the states [4) and (0) are given by y(x) and Q(x), respectively. Derive the expression for the inner product (14) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? 2. Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states (4) and (o) are orthogonal: (014) = 0. (x) M Figure 1 3. Assume a particle has a wave-function y(x) sketched in Fig. 2. Sketch the wave- function (p) of this particle in momentum representation. (x) Figure 2 4. Consider the state |p) which is the eigenstate of the momentum operator o such that plp) = plp) (eq 1). We also know that if the state ) has a wave-function (x) then the wave-function of 10) = ply) is $(x) = -ihy(x)/x (eq 2). Use (eq 1) and (eq 2) to derive an explicit form of the wave-function of p) in the coordinate representation. Neglect the normalization constant.

Answer 1

is a 1. Ware function. Have function in quantum physics mathematical description of the quantum state of an isolated quentum system. <4147= 19*u4ta) dix 140x11² represents the probability of finding the particle at position a. $49) A Inner product of both will be zero. As cut any point one is finite but other is zero. 3. 1466) can be calculated as ipa/5 446) = वर sent 늪 e

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