Department of Studies in Physics
Davangere University, Davangere
Introduction to Quantum
Mechanics
Ms. Soumya S Bulla
Assistant Professor
We are what we repeatedly do. Excellence, then, is not an act, E-Mail: Soumyabulla@gmail.com
but a habit- Aristotle
Contact Number:+91 80882-69242
What is Light?
• When it comes to light, the evidence presents
us with a paradox. It propagates through space
as a continuous wave but somehow exchanges
its energy in the form of discrete particles. So,
“wave” or “particle”—what is light?
• At the end of the nineteenth century, physics consisted essentially of classical
mechanics, the theory of electromagnetism, and thermodynamics.
Classical mechanics dynamics of material bodies
Maxwell’s electromagnetism proper framework to study radiation
matter and radiation were described in terms of particles and waves,
respectively.
Lorentz force or by thermodynamics interactions between matter and
radiation
At the turn of the twentieth century, however, classical physics, which had been quite
unassailable, was seriously challenged on two major fronts:
• Relativistic domain: Einstein’s 1905 theory of relativity showed that the validity of
Newtonian mechanics ceases at very high speeds (i.e., at speeds comparable to that of light).
• Microscopic domain
Failures of Classical Mechanics
The failure of classical physics to explain several microscopic phenomena—such as
blackbody radiation, the photoelectric effect, atomic stability, and atomic spectroscopy
—had cleared the way for seeking new ideas outside its purview.
• 1900- Max Planck introduced the concept of the quantum of energy BBR.
• 1905- Einstein provided a powerful consolidation to Planck’s quantum concept
photoelectric effect
• Bohr introduced in 1913 his model of the hydrogen atom.
• Then in 1923 Compton made an important discovery that gave the most conclusive
confirmation for the corpuscular aspect of light.
This series of breakthroughs—due to Planck, Einstein, Bohr, and Compton—gave both the
theoretical foundations as well as the conclusive experimental confirmation for the particle
aspect of waves; that is, the concept that waves exhibit particle behavior at the microscopic
scale. At this scale, classical physics fails not only quantitatively but even qualitatively and
conceptually.
de Broglie introduced in 1923 another powerful new concept that classical physics could not
reconcile:
He postulated that not only does radiation exhibit particle-like behavior but, conversely,
material particles themselves display wave-like behavior and confirmed experimentally in
1927 by Davisson and Germer; they showed that interference patterns, a property of waves,
can be obtained with material particles such as electrons.
Historically, there were two independent formulations of quantum mechanics.
1. Matrix mechanics, was developed by Heisenberg (1925) to describe atomic structure starting
from the observed spectral lines.
2. Wave mechanics, was due to Schrödinger (1926); it is a generalization of the de Broglie
postulate. This method, more intuitive than matrix mechanics, describes the dynamics of
microscopic matter by means of a wave equation, called the Schrödinger equation;
Dirac then suggested a more general formulation of quantum mechanics which deals with
abstract objects such as kets (state vectors),bras, and operators.
Position or
Schrödinger’s
Continuous Momentum
wave
Dirac basis representations
mechanics
formulatio
Heisenberg’s
n Discrete basis matrix
formulation
Combining special relativity with quantum mechanics, Dirac derived in 1928 an equation which
describes the motion of electrons. This equation, known as Dirac’s equation.
In summary, quantum mechanics is the theory that describes the dynamics of matter at the
microscopic scale.
Fine! But is it that important to learn?
This is no less than an otiose question, for quantum mechanics is the only valid framework for
describing the microphysical world. It is vital for understanding the physics of solids, lasers,
semiconductor and superconductor devices, plasmas, etc.
In short, quantum mechanics is the founding basis of all modern physics: solid state, molecular,
atomic, nuclear, and particle physics, optics, thermodynamics, statistical mechanics, and so on. Not
only that, it is also considered to be the foundation of chemistry and biology.
