Download Introduction to Quantum Mechanics

Introduction to Quantum Mechanics
Quantum Mechanics arose as a result of problems that were becoming evident with
classical physics in the late 1800’s and early 1900’s. These problems are as follows:
1. Blackbody Radiation. Blackbody radiation is the radiation that is given off by
solids in equilibrium with their surroundings. This intensity of the radiation is a
function of temperature and wavelength. Classical physics attempted to solve this
problem but resulted in “ultraviolet catastrophe” because the leading classical
theory describing blackbody radiation predicted an infinite amount of energy
being emitted at short wavelengths. This calculation is based on classical physics
in which the vibrating atoms were modeled as harmonic oscillators with a
spectrum of normal modes frequencies and a continuum of allowed energies. It
became clear that classical physics was not accurately representing nature.
In 1901, Max Plank found a solution to this problem by postulating that the energies of
the harmonic oscillators were quantized or restricted to values:
En  n n=0,1,2...
where  =1.055 x 10-34Joules which is now called Plank’s constant.
In 1905, Albert Einstein went one giant step further to explain the photoelectric effect in
which electrons were emitted from the surface of metals when light was incident on the
surface. He postulated that light itself was composed of particle-like quanta called
“photons” with an energy:
E  h
In the mid-1920’s de Broglie argued that if light had particle properties, then particles
had light or wave-like properties and speculated that particles had a certain wavelength:
p
h

This set the stage for Schrodinger in 1926 to propose his famous wave equation.
Bohr Atom
In 1913, Niels Bohr proposed a model for the atom that cleared up several unresolved
problems such as the existence of descrete spectral lines and the fact that electrons in
circular orbits as proposed by Rutherford didn’t decay into the nucleus. Bohr proposed
that the angular momentum of the electrons is quantized:
Ln  mvrn  n
n=1,2,3
From this equation, it is simple to derive that the energy levels are quantized with
energies:
13.6
eV
n2
Bohr explained that the electrons could only be in these allowed states and not in any
intermediate states. Furthermore, the descrete spectral lines were caused by electrons
making a transition from one of these acceptable states to another.
En  
Schrodinger’s Equation
In 1926 Schrodinger proposed his famous wave equation and described the hydrogen
atom. There are five postulates of quantum wave mechanics:
1. There exists a wavefunction 