the explanation to part a-d is given in the attached file
The Schrodinger equation for a particle in a ring can be expressed as H cap psi(phi)...
For a particle in a ring, the energy levels can be expressed as En= [(h)2/ (2m)] [(n)/(L)]2 where n= 0, ±1, ±2, …, L = 2πr is the circumference of the ring, and r is the radius of the ring. If r=4.0 x 10-10 m, find the energy and the corresponding wavelength (λ) for the n = 0 to n=1 transition.
Can anyone help me to solve this question on Quantum Mechanics about Schrodinger equation please? 1. (a) From the definitions of probability density and flux, P(x,t) = 4*(x,t){(x,t) (:9 = 2 show that ƏP(x,t) at @j(x,t) Ox GP(x,t) for a particle satisfying the Schrodinger equation iħ – I hº o°F(x,t). ?+V(x)*(x,t) am Ox? at provided that the potential V(x) is real..
JO) A Pi- electron in benzene molecule may be described in quantum com make the assumption that benzene is circular. In such a case, the potential energy is constant (1.e. V =0) and Schrodinger equation for a particle of mass me constrained to move on a circle of radius a is: (-h7/8 Tma)dade - Em for 0 SOS 27. Here is the angle that describes the position of the particle (i.e. pi-electron) around the ning a) Show that the solution...
4. Estimate the transition frequency for the poryphyrin molecule from m-11 to m 12, assuming that the pi electrons can be modeled as a particle in a ring of radius 440 picometers. (C 7. The most probable distance of the electron from the nucleus in a 1ls state hydrogen atom (with wavefunction V1) can be determined by 21. A (A) solving the eigenvalue equation: Rvw rV., finding the maximum in the 1s radial distribution function by differentiation. (C) substituting vi,...
Scattering #1 Consider the "downstep" potential shown. A particle of mass m and energy E, incident from the left, strikes a potential energy drop-off of depth Vo 0 (2 pts) Using classical physics, consider a particle incident with speed vo. Use conservation of energy to find the speed on the right vf. ALSO, what is the probability that a given particle will "transmit" from the left side to the right side (again, classically)? A. B. (4 pts) This problem is...
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...
A particle moves and has a potential energy that can be described by the equation U(x) = 4 sin(2 x) where U(x) is in J. The total energy of the particle is E_tot = 2 J. Make a well-labelled graph of U(x)vs. x from x = 0 to x = pi. Draw a line corresponding to E_tot on your diagram. Assume the particle is moving in the positive x direction. Where is the particle speeding up? Make sure you solve...
Question 8 please 5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write the time derivative as 2.4(x, t) = V(x,+) - (xt), where At is a sufficiently small increment of time. Plug the algebraic form of the derivative into Schrodinger's Eq. and solve for '(x,t+At). b. Put your answer in the form (x,t+At) = T '(x,t). c. What physically does the operator T do to the function '(x,t)? d. Deduce an expression for '(x,t+24t), in terms...
1- 5. Two particles each of mass m are fixed at the end of a rigid rod of length 2a. This rod lies in the xy plane and is free to rotate in that plane about an axis passing through the midpoint of the rod and perpendicular to it (that is, parallel to the z-axis). Neglect the inertial properties of the rod in the rest of this question z-axis 1. Derive the classical expression for the kinetic energy of the...
1- 5. Two particles each of mass m are fixed at the end of a rigid rod of length 2a. This rod lies in the xy plane and is free to rotate in that plane about an axis passing through the midpoint of the rod and perpendicular to it (that is, parallel to the z-axis). Neglect the inertial properties of the rod in the rest of this question z-axis 1. Derive the classical expression for the kinetic energy of the...