Under what conditions can the three-dimensional time-dependent Schrodinger equat
ID: 1998418 • Letter: U
Question
Under what conditions can the three-dimensional time-dependent Schrodinger equation be separated into time-only and space-only equations. Under what conditions can the three-dimensional time-independent equation be separated into radial and angular equations? Why do the eigenfunctions of the 3-D TISE have three indices (quantum numbers)? What physical observables do each of these quantum numbers correspond to? Why must phi(phi) be single-valued? Why must m = integer? Why must |m| lessthanorequalto l? What are the restrictions on the possible values of l? What is the source of these limits? The solutions to the angular portions of the 3-D are the spherical harmonics, built up from the Legendre polynomials and associated Legendre functions. What are the shapes and symmetries of the associated Legendre functions? What quantum numbers are relevant for these solutions? Many systems (diatomic molecules, for example) are NOT spherically symmetric, yet we often use the spherical harmonics as a basic set to describe the angular part of the wave function for these systems. Why is this possible?Explanation / Answer
schrodinger wave equation in general is used to determine the allowed values of energy of a system. also the wave function is used to determine the values of probbaility.
schrodinger equation can be seperated into time-only and space only equations if we determined to describe the position of a particle or allowed values of energy in a one dimensional box. we take the time and space equations only in the case of particles tarpped in a box.
on the other side, we take the schrodinger euqatio in radial and angular part if we determined to solve for atoms like hydrogen,helium. if the radial parobbaility is to be deterined, then we take the radial part of schrodinger equation. else we consider the complete schrodinger equation.
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