Can I get the solution for these Atomic & Quantum Mechanics Physics problems?

Textbook: Introduction to Quantum Mechanics, 2nd edition, by David J. Griffiths (Pearson Prentice Hall, Upper Saddle River, NJ, 2005).

1. A complex number z is written in standard form when it is expressed as z = a + ib for two real numbers a and b. Let z* denote the complex conjugate of z. When z is written as z = rell, for real numbers r and 0, it is said to be written in polar form. 1. Suppose z = -13 + 2i. Work out z in polar form. 2. For the same z, work out 21/5 in standard form. 3. For two complex numbers z and z2, prove that (2122)* = zizz. 4. Give an argument based on calculus for why cos + isin 0 = end when 0 is real. 5. Evaluate fo e " cos? x da by using complex-number methods (no trig identities). 2. Start with the factorizable solutions to the time-dependent Schrodinger equation WE(x, t) = DE(x)ein where the E(x) are normalized eigenfunctions for H with eigenvalues E. Use this to explain why the most general solution to the time-dependent Schrodinger equation can be written as 2/ ( 2 , t ) = e- K Hub (x, 0) . 3. On occasion, one might be tempted to take a particle's potential energy to be propor- tional to its very wave function. I.e., that if (x), then V(x) = cy(x). This means that upon writing the time-independent Schrodinger equation, one would need to solve 2 n dx2 4 (x) + cy (x ) 2 = Ev (x ) . There is a fundamental problem with this. What is it? 4. Let In(x), n = 0, 1, 2, . .. be solutions to the time-independent Schrodinger equation for a harmonic oscillator of frequency w (not that we have studied harmonic oscillators completely yet). Suppose that a particle in this potential has a wave function I ( x , t ) = $h(x) e-izwt for some k. If a measurement of the particle's energy is made, what energy value will be found?5. Let & and p be the position and momentum operators, and consider the operator C =-i(xp -px) . Is C a linear or nonlinear operator? Let v(x) be any normalized wave function and consider C's action on it, i.e., Cy(x). Prove that C's action can be greatly simplified over the basic definition above. What then is Cu(x) equal to? 6. At one step in the proof of Ehrenfest's theorem, we made use of the fact that at 2x + 2 + 02 20 dx = / at Ox Ox at dx . How was that step justified? 7. Recall the normalized solutions for the time-independent Schrodinger equation for an infinite square well with walls at 0 and L: 20n ( 20 ) = 1 nTX sin L n = 1, 2, 3, ... . Why, for any angle d, is a valid wave function for a particle in the well at t = 0? There are two reasons. Prove your assertion. Next: What is the expectation value for p when (x) is the particle's wave function? The closer you get to the final answer, the more partial credit I'll give. (Hint: Remember what you learned about (p) for the stationary states un (x) from the Griffiths homework problem.)