Solve the following questions below.

Consider the wave function [shown below]: of the 11. = 4 state of the particle conned in a box. 9 The probability density is lowest at I = % and I = %. G the probability density is one at :1: = ETL. D The probability density is constant inside the box. 0 The highest value otthe probability density is %_ 4.1. Figure 4.29 shows four wave functions in the region x > 0. Indicate for each wave function whether the wave function is an acceptable or unacceptable wave function for an actual physical system. If the wave function is not acceptable, explain why. AAA : HY Figure 4.29 Four possible wave functions.4. Consider the normalized wave function 15 V16 (1-x' ). This wave function is non-zero when - I s x 2 1. This means the wave function is zero at 1 and -1. a. Show that this wave function is normalized. Hint, integrate it between -1 and 1. b. Using this wave function find the average value of x. Ans. 0. v = 0.1 and 0.2 nm.10. Consider the random variable X with the probability density function f(x; 1, 0') = for x > 0 (a) Using the probability density function of X show that E(X) =e 2 (b ) Derive the probability density function of Y=In X