# Central potential and 3 dimensional Schrodinger equation

Not what you're looking for?

The Central Potential

The 3-D time independent Schrodinger equation for a particle of mass m in a spherically symmetric potential is

-- Equation----

a) By writing grad^ in terms of r, theta and phi show that this can be written as

-- Equations---

(b) Writing shi = R Y show that Y must satisfy L^2 Y = c Y where c is a constant, and where

-- Equation----

(c) Writing R = f(r)/r, show that f(r) satisfies the equation

-- Equation----

(d) This is of exactly the same form as a 1-D time independent Schrodinger equation with V replaced by V + c/2mr^2. So can we conclude that the spectrum in the original 3D problem is the same as for this 1D problem?

##### Purchase this Solution

##### Solution Summary

Solution is very detailed. Every step of the solution has been shown clearly. I have used equation editor to type in equations. Hence, the typing and clarity of the solution is similar to what you would find in a textbook.

##### Solution Preview

Following is the text part of the 5-page solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear here. Thank you for using Brainmass.

================================================================

(a)

...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### The Moon

Test your knowledge of moon phases and movement.

##### Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

##### Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

##### Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

##### Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.