question 5 please 5. A free particle has the following wave function at t = 0:V(x, 0) = Ne- -a|x|=So0Ne-axNeaxwhere N and a are real, positive constants.a) Normalize this wave function.b) Determine Ax by finding (x) and (x²). You can simplify the work by using symmetry (for example, if the wave functionis symmetric around x = 0 what do you expect (x) to be?). The following integral could be useful:-bx dxxme=m!fm+1x > 0x < 0c) What is the expectation value of the momentum, (p)?d) We can represent this wave function at t = 0 as a superposition (linear combination) of complex exponentials:(x,0) = Ne-a|x| =[ A(k)etkx dk-∞Determine the amplitude function A(k).e) Find an expression for (x, t). You can leave your answer in the form of an integral over k but make sure all dependenceon k is made explicit.Optional: this choice of wavefunction V(x, 0) is really just for practice with calculating some expectation values, normal-ization, etc, but it's actually a BAD choice for a wavefunction. Why is it a bad choice? Why might it fail at being arealistic wavefuction?

Answered: Image /qna-images/answer/04a264d8-e22b-457b-a973-0feca557f398.jpg

5. A free particle has the following wave function at t = 0: V(x,0) = Ne-a|x| = [Ne-ª* x>0 Near x < 0 where N and a are real, positive constants. a) Normalize this wave function. b) Determine Ax by finding (x) and (x²). You can simplify the work by using symmetry (for example, if the wave function is symmetric around a = 0 what do you expect (x) to be?). The following integral could be useful: 1. me -bx dx = m! fm+1

5. A free particle has the following wave function at t = 0: V(x,0) = Ne-a|x| = [Ne-ª* x>0 Near x < 0 where N and a are real, positive constants. a) Normalize this wave function. b) Determine Ax by finding (x) and (x²). You can simplify the work by using symmetry (for example, if the wave function is symmetric around a = 0 what do you expect (x) to be?). The following integral could be useful: 1. me -bx dx = m! fm+1