2. Contents
Hydrogen Atom
Two particle problem
Seperation of energy as transational and rotational
The R and Equations
Introduction to the four quantum numbers and their interdependence on the
solutions of the three equations
3. Hydrogen Atom
The Hydrogen atom consists of an electron and a proton.
We shall assume electron and proton to be point masses whose interactionsis
given by coulomb’s law
−𝑧𝑒2
/4Π𝜀𝑜𝑟
Z is the atomic no. ; 𝜀𝑜 is the permittivity of the vaccums
Since the electron is very much faster than the nuclear particles, it is assumed that
the nucleus is stationary as compared to the electron
Thus, Schrodinger equation for the hydrogen atom will be the equation for a single
electron moving around the nucleus.
Thus, [−ℎ2/8Π2me 2
+ V] (x y z) = E(x y z)
4. Separation of variables
In order to solve the previous given
equation, the Cartesian co ordinates
are converted to r as,
X = r sin cos
Y = r sin sin
Z = r cos
And 𝑥2
+ 𝑦2
+ 𝑧2
=𝑟2
The transformation of Cartesian co-
ordinates in equation into spherical
polar co-ordinates gives:
14. Questions
Use the method of separation of variables to breakup the Schrodinger equation for
a rigid rotor to ordinary angular equation.
Obtain Radial Wave Equation From the Schrodinger wave equation for spherical co
ordinates
Justify the terms Principle, Azimuthal and magnetic quantum number for n, L, and
M respectively
15. Reference
Quantum Chemistry by Ira N. Levine
Fundamentals of Quantum Chemistry by R. Anantharaman
Quantum Chemistry by Tamas veszpremi and Miklos Feher