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We know that there is a relativistic version of Schrodinger equation called Klein-Gordon equation. However, it has some problems and due to these problems, there is Dirac equation that handles these problems. So, the question is, if there is a solution that is allowed by Klein-Gordon, but not by Dirac, can this solution be considered valid? Also, can Dirac equation be used for spin-0 particles?
an electron may freely move on a ring with a radius r, the schrodinger equation for this problem Problem 4 (2.0 points) An electron may freely move on a ring with a radius r. The Schrödinger equation for this problem is: 0=2/2 t? 2² 2mr2 2023 SV() = Ey() (4.1) where the azimuthal angle o characterizes the position of the electron. (a) A general form of the wave function is y (0) = A MO. (4.2) Show that Eq. (4.2)...
Solution of the Schrodinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron Each function is characterized by 3 quantum numbers: n, I, and my Seronger If the value of n=1 The quantum number / can have values from to The total number of orbitals possible at the n-1 energy level is If the value of 1=3 The quantum number my can have values from to The total number...
2. There are many mathematical acceptable solutions to the Schrodinger equation for a system, but only certain are physically acceptable because..... a. Physically acceptable wave functions must be finite, single valued, and continuous with continuous first derivative b. All wave functions must be complex c. All physical quantities are real d. All solutions must be eigenfunctions of the momentum operator
1 write the Schrodinger equation in: a. Original form b. Operator form. c. Write the equation for the operator used. d. Name three important types of information obtained by solving the Schrodinger wave equation. e. Can this equation be solved accurately and completely for H-atom and H2 molecule? Explain briefly your answer.
Prove the following function (using -i) is a solution to the Schrodinger equation and determine its energy. 1/2 8Tt 1/2 8Tt
10) The wave functions obtained by solving the Schrodinger equation for the simple harmonic motion is: v.(E) = A e-y-2/2 (y). Here y = (a)"25, normalization constant A = [(a/ 2/(2" n!)]"2 and n=0, 1, 2, ... are the vibrational quantum numbers. H.(y) is the Hermite polynomial and it is defined as: Hly)= (-1)" ey^2 (d" e-y^2? (dyn J a) Calculate the fourth (i.e. n = 3) wave function, using the above formulas.
The Schrodinger equation for a particle in a ring can be expressed as H cap psi(phi) = E psi(phi), where H cap = -h^2 partial^2/21 partial phi^2; psi(phi) = 1/squareroot 2 pi e^-ik phi, k is an integer What is the potential energy? What is the kinetic energy? Write the Schrodinger equation Derive the eigenvalue Show that psi(phi) = psi(phi + 2 pi) Derive an expression for the probability density for a particle in a ring?
a) Set up the Schrodinger equation for a particle in an infinite square well where: V = 0 -a<x<a V= otherwise b) Solve the equation to find E and the wave function
determine whether the wavefunction for a particle in a 2d box eigenfunction (using Schrodinger equation)