11. 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 4nrdr = dt.
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- I solved it but I need help in two parts.For first part, How to show thev formula is a solution of ODE? Second, for the third part, how to show it is bounded because I can not integratw matrix?By employing the prescribed definitions of the raising and lowering operators pertaining to the one-dimensional harmonic oscillator: x = ħ 2mω -(â+ + â_) hmw ê = i Compute the expectation values of the following quantities for the nth stationary staten. Keep in mind that the stationary states form an orthogonal set. 2 · (â+ − â_) [ pm 4ndx YmVndx = 8mn a. The position of particle (x) b. The momentum of the particle (p). c. (x²) d. (p²) e. Confirm that the uncertainty principle is satisfied for all values of nNeed full detailed answer.
- 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).O Consider the kinetic energy matrix elements between Hydrogen states (n' = 4, l', m'| |P|²| m -|n = 3, l, m), = for all the allowed l', m', l, m values. What kind of operator is the the kinetic energy (scalar or vector)? Use this to determine the following. For what choices of the four quantum numbers (l', m', l, m) can the matrix elements be nonzero (e.g. (l', m', l, m) (0, 0, 0, 0),...)? Which of these nonzero values can be related to each other (i.e. if you knew one of them, you could predict the other)? In this sense, how many independent nonzero matrix elements are there? (Note: there is no need to calculate any of these matrix elements.)