(a) Write out the wave functions ?? ?(?, ?) for ?1 −1 and ?2 0 . Show that these wave functions are normalized. (b) What are the average values for 〈?? 〉 and 〈? 2 〉 for these two wave functions? (c) Which of these two wave functions is cylindrically symmetric (i.e. symmetric about the z-axis)? (d) Sketch these two wave functions in the xz plane, using polar-like coordinates of |?? ?| as a function of ?.
Physical chemistry question!!!! Please help!!!!! Write out the complete wave functions for a 2p_0 orbital and a 2p_1 orbital. Show that the full wave function for a 2p_1 orbital is normalized. Find the most probable position and the average position of an electron in a 2p_0 orbital.
Show that the Hartree-Fock guess wave function for helium \,(x1,x2) = 7*1*(z)(ra)ya(z) (02) [(5.), (S.2) – 4,(S-2)". (S...)] is properly normalized. Note that you must integrate over the coordinates and sum over the two values cach S. variable can assume.
(a) Write down wave functions that describe the behavior of the particle in region 1, region 2, and region those coefficients and explain why they are equal to zero. Write down the expression of ?? as well. ?? (b) Sketch the probability distributions you would expect for the ground state and the first excited state. (c) Use the continuity conditions at x = 0 to show how the coefficients of the wave function in region 2 are related to the...
particle in a cylindrically symmetric potential: do only C please 3. Particle in a cylindrically symmetrical potential: Let pw. be the cylindrical coordinates of a spinless particle (z = pcos y, y psiny: P 20, OS <2m). Assume that the potential energy of this particle depends only one, and not on yor: Vin-V ). Recall that & P R 1 18 dr2 + dy? - apa pap + 2 day? (a) Write, in cylindrical coordinates, the differential operator associated with...
1. Spherical waves. Starting with the wave equation VE in spherical polar ,,2 2.1 in spherical polar coordinates, and letting E E(r,t) only, show that where f and g are arbitrary functions. (Hint: start by writing E- F/r and substitute into the wave equation to get a differential equation in the function F(r.t).) What does each term represent physically, and what is the significance of the factor /r? (Hint: think Poynting vector.) 1. Spherical waves. Starting with the wave equation...
Written Question #2: For the electromagnetic wave propagating out of the page from problem #1, assume that the magnetic fields, directions are along the x-axis (positive values of B are along the positive z-axis and vice versa). (a.) What direction is the wave's electric fields? Explain how t 0 you determined your answer (b.) For the z = 0 location, sketch both the electric and magnetic field vectors for the indicated times. Draw the peak electric and magnetic field vectors...
4.(10pts) Write Laplaces' equation in cylindricaol co-ordinates(p527 ex.3,use pinstead ofr) Assume the solution, e, φ, z), n can be written φ (p, φ, z)s u(p, φ)e-kz and Show that the equation for u is the two dimensional wave equation; Written in polar co-ordinates:xpcosp,y psinp For a plane wave traveling in a direction defined by:4-kcosce, ky-kinα Show that the plane wave solution can be written; look for a solution u z(x)en (2-n212,-0 And the equation for Z, is Bessels equation:Zh "x2...
Particle in a cylindrically symmetrical potential Let p, o, z be the cylindrical coordinates of a spinless 1. (x = ? coso, y = ? sin ?, p 0, 0 <p < 2?). Assume that the potential en of this particle depends only on , and not on ? and z. Recall that: a. Write, in c ylindrical coordinates, the differential operator associated with the Hamiltonian. Show that H commutes with L, and P. Show fr the wave functions chosen...
1. The wave-functions of the states [4) and (0) are given by y(x) and Q(x), respectively. Derive the expression for the inner product (14) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? 2. Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states (4) and (o) are orthogonal: (014) = 0. (x) M Figure 1 3. Assume a particle has a wave-function y(x) sketched in Fig. 2....
1. The wave-functions of the states [4) and (0) are given by y(x) and Q(x), respectively. Derive the expression for the inner product (14) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? 2. Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states (4) and (o) are orthogonal: (014) = 0. (x) M Figure 1 3. Assume a particle has a wave-function y(x) sketched in Fig. 2....