##### show all steps thoroughly (sorry for my bad grammar)
This is the required expectation value.
##### show all steps thoroughly (sorry for my bad grammar) Assume that electron in state have wave function of spherical coordinate 4π Where g(r) wave function in part of radius By (r)|-r-dr = 1)show...
##### show all steps thoroughly (sorry for my bad grammar) Assume that electron in area electric field of proton and in the state wave function r + 2p2 1,0.0 1) Find expectation value of energy 2) Find expectation value of angular momentum squared (L2) 3) Find expectation value of angular momentum in component axis -Z L) 4) How much angular momentum in component axis-Z will probability of found particle? And why? Assume that electron in area electric field of proton...
(1) The ground-state wave function for the electron in a hydrogen is given by ls 0 Where r is the radial coordinate of the electron and a0 is the Bohr radius (a) Show that the wave function as given is normalized (b) Find the probability of locating the electron between rF a0/2 and r2-3ao/2. Note that the following integral may be useful n! 0 dr =-e re /a roa r a Ta
Consider an electron whose wave function is ?(r,0,?)-- e* sin ? + cos ?)f(r). 47t where I (rrr2dr-| , and ?, ? are the azimuth and polar angles, respectively. (i) Rewrite the wave function in terms of the appropriate spherical harmonics. (4 marks) (ii) What are the possible measurement results of the z-component L, of the angular momentum of the electron in this state? (6 marks) (iii) Calculate the probability of obtaining each of the possible results in part (i)....
Consider a particle of mass m in an infinite spherical potential well of radius a For write down the energies and corresponding eigen functions ψ--(r,0.9). (3 pt) a) ne that at t-o the wave function is given by o)-A. Find the normalization constant A function in this basis. Solve for the coeffici You may find useful the integrals in the front of the (6 pt) d) Now consider the finite potential spherical well with V(r)- ing only the radial part...
Assume that we have three independent observations: where Xi ~ Binomial(n 7,p) for i E { 1.2.3). The value of p E (0, 1) is not known. When we have observations like this from different, independent ran- dom variables, we can find joint probabilities by multiplying together th ndividual probabilities. For example This should remind you the discussion on statistical independence of random variables that can be found in the course book (see page 22) Answer the following questions a...