-
Quantum Mechanics: Stationary Perturbation Theory
10 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
Stationary perturbation theory is concerned with finding the changes in the discrete energy levels and the changes in the corresponding energy eigenfunctions of a system, when the Hamiltonian of a system is changed by a small amount. In this section we provide reading material regarding...
-
Quantum Mechanics: Time-Dependent Perturbation Theory
10 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
Time-dependent perturbation theory, developed by Paul Dirac, studies the effect of a time-dependent perturbation V(t) applied to a time-independent Hamiltonian H0. Since the perturbed Hamiltonian is time-dependent, so are its energy levels and eigenstates. Therefore, the goals of time-dependent...
-
Quantum Mechanics: Harmonic Oscillator
09 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
The quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator. It is one of the most important model systems in quantum mechanics because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point....
-
Quantum Mechanics: WKB Approximation
09 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
In physics, the WKB (Wentzel–Kramers–Brillouin) approximation, also known as WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) approximation, is the most familiar example of a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically...
-
Quantum Mechanics: Hydrogen Atom and Electron Spin
09 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force. The most abundant isotope, hydrogen-1, protium, or light hydrogen, contains no...
-
Quantum Mechanics: Landauer's Formula
08 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
When a metallic nanojunction between two macroscopic electrodes is connected to a battery, electrical current flows across it. The battery provides, and maintains, the charge imbalance between the electrode surfaces needed to sustain steady-state conduction in the junction. This static...
-
Quantum Mechanics: Periodic Potentials and Kronig-Penney Model
09 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
The Kronig-Penney model is a simple approximation of a solid. The potential consists of a periodic arrangement of delta functions, square well or Coulomb well potentials. By means of epitaxial growth techniques artificial semiconductor superlattices can be realized, which behave very similar to...
-
Quantum Mechanics: Tunneling
08 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
In quantum mechanics, quantum tunnelling is a micro nanoscopic phenomenon in which a particle violates the principles of classical mechanics by penetrating a potential barrier or impedance higher than the kinetic energy of the particle. A barrier, in terms of quantum tunnelling, may be a form of...
-
Quantum Mechanics: Time Independent Schrodinger Wave Equation
07 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
In physics, especially quantum mechanics, the Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time. It is as central to quantum mechanics as Newton's laws are to classical mechanics.In the standard interpretation of quantum mechanics, the...
-
Quantum Mechanics: Introductory Concepts
07 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck, David K. Ferry
In this section of the Quantum Mechanics class we discuss the particle-wave duality and the need for the quantization of energy to explain the black-body radiation and the photoelectric effect. We provide reading material, slides and video, which in a very illustrative way, explain the most...
-
Quantum Mechanics: Postulates
07 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
A physical system is generally described by three basic ingredients: states; observables; and dynamics (or law of time evolution) or, more generally, a group of physical symmetries. A classical description can be given in a fairly direct way by a phase space model of mechanics: states are points...
-
Quantum Mechanics: Wavepackets
07 Jul 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
In physics, a wave packet is an envelope or packet containing an arbitrary number of wave forms. In quantum mechanics the wave packet is ascribed a special significance: it is interpreted to be a "probability wave" describing the probability that a particle or particles in a particular state will...