Consider the function y(φ)-e",-ie h2 d where I is a constant? If so, what is the a) Is it an eige...
* Let φ : R3-+ R be a continuous function. The level sets of φ are the sets 4:-{(z, y, z) e R3 Id(z, y, z) =c); where c is a real constant (c) Use the setup in this problem to argue that a sequence on the unit sphere x E R31 (- is the standard Euclidean norm) cannot converge to a point that is not an element of the unit sphere. * Let φ : R3-+ R be a...
16. Problem 16. Consider a composite system characterized by a joint probability density function given by, def The constant ξ is a real normalization factor and pxy is defined on the two-dimensional planar region DCartesian def where Rt denotes the set of strictly positive real numbers. a) Define the set Dpolar representing DCartesian recast in polar coordinates (r, ); b) Performing a change of coordinates (namely, from Cartesian to polar coordinates), find the expression of the new joint probability density...
(a) Show that (@) = sin e- is an eigenfunction of both Î, and Î", where = -1 1 a 1 22 sin + sin 020 sin0 and derive the corresponding eigenvalues. You may use the identity 1 a 1 sin sin 2 sin sin 0 80 sino 31 (sin 00 (5 marks) (6) Consider the function $(,0,4)= A - 1/200 sin 6e-ip, 20 where A is a constant and an is the Bohr radius. This is a hydrogen atom...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
Find fY(y) from the domain: Consider the domain D={(x,y): 0 < x < 1,-x < y < x} and let fix, y)=cx,where c is a constant. 1.1 (4.6 marks) To start with, we wish you to determine c such that f(x, y) a joint density of random vector (X, Y) that takes values on D. order to do that, you must first calculate fix, y) dA where dA is an area element of D, and then deduce c Hence you...
Would like to get help with this homework, and I will be so thankful if you solve all the questions and if that's a lot start from number 4, please. It is hard this why I am asking for your help if you answer all my questions I will give you a good rating and feedback. Thank you so much for your help. Atomic Orbitals, Bonds and Dispersion Forces pictures of atomic orbitals such as those above. The color sign...