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- Show that the following wave function is normalized. Remember to square it first. Limits of integration go from -infinity to infinity. DO NOT SKIP ANY STEPS IN THE PROCEDURE11. Evaluate (r), the expectation value of r for Y,s (assume that the operator f is defined as "multiply by coordinate r).Why does (r) not equal 0.529 for Y,,? In this problem,use 4ardr = dt.Please don't provide handwritten solution ..... Determine the normalization constant for the wavefunction for a 3-dimensional box (3 separate infinite 1-dimensional wells) of lengths a (x direction), b (y direction), and c (z direction).
- 4.3 A particle with mass m and energy E is moving in one dimension from right to left. It is incident on the step potential V(x) = 0 for x 0, as shown on the diagram. The energy of the particle is E > Vo. = V(x) V = Vo V=0 x = 0 (a) Solve the Schrödinger equation to derive 4(x) for x 0. Express the solution in terms of a single unknown constant. (b) Calculate the value of the reflection coefficient R for the parti- cle.4.5 Consider reflection from a step potential of height Vo with E > Vo, but now with an infinitely high wall added at a distance a from the step (see diagram): V(x) E V = Vo V = 0 x = 0 x = a x (a) Solve the Schrödinger equation to find v/(x) for x < 0 and 0 ≤ xa. Your solution should contain only one unknown constant. (b) Show that the reflection coefficient at x = 0 is R = 1. This is different from the value of R previously derived without the infinite wall. What is the physical reason that R = 1 in this case? (c) Which part of the wave function represents a leftward-moving particle at x < 0? Show that this part of the wave function is an Solutions of the one-dimensional time-independent Schrödinger equation 103 eigenfunction of the momentum operator, and calculate the eigen- value. Is the total wave function for x ≤ 0 an eigenfunction of the momentum operator?Needs Complete solution with 100 % accuracy.