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Quantum Mechanics: WKB Approximation

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09 Jul 2008 | Series | 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: Wavepackets

07 Jul 2008 | Series | 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...

Quantum Mechanics: Tunneling

08 Jul 2008 | Series | 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-Dependent Perturbation Theory

10 Jul 2008 | Series | 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: Time Independent Schrodinger Wave Equation

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: Stationary Perturbation Theory

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: Postulates

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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: Periodic Potentials and Kronig-Penney Model

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: Landauer's Formula

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: Introductory Concepts

07 Jul 2008 | Series | 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: Hydrogen Atom and Electron Spin

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: Harmonic Oscillator

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 for Engineers: Podcasts

This course will introduce the students to the basic concepts and postulates of quantum mechanics. Examples will include simple systems such as particle in an infinite and finite well, 1D and 2D harmonic oscillator and tunneling. Numerous approximation techniques, such as WKB method,...

Process Modeling

23 Aug 2011 | Series | Contributor(s): Dragica Vasileska

This series on process modeling describes key process modeling steps such as implantation, diffusion, oxidation, etching, deposition, etc.

PN Junction Theory and Modeling

14 Sep 2005 | Series | Contributor(s): Dragica Vasileska

This set of lecture notes is intended to help students learn the basics of PN junction theory and modeling.

Nanoelectronics and Modeling at the Nanoscale

30 Jun 2011 | Series | Contributor(s): Dragica Vasileska, Gerhard Klimeck

Nanoelectronics refers to the use of nanotechnology on electronic components, especially transistors. Although the term nanotechnology is generally defined as utilizing technology less than 100 nm in size, nanoelectronics sometimes refers to transistor devices that are so small that inter-atomic...

Modeling Single and Dual-Gate Capacitors using SCHRED

31 Mar 2006 | Series | Contributor(s): Dragica Vasileska

SCHRED stands for self-consistent solver of the 1D Poisson and 1D effective mass Schrodinger equation as applied to modeling single gate or dual-gate capacitors. The program incorporates many features such as choice of degenerate and non-degenerate statistics for semiclassical charge description,...

From Semi-Classical to Quantum Transport Modeling

09 Aug 2009 | Series | Contributor(s): Dragica Vasileska

This set of powerpoint slides series provides insight on what are the tools available for modeling devices that behave either classically or quantum-mechanically. An in-depth description is provided to the approaches with emphasis on the advantages and disadvantages of each approach. Conclusions...

Computational Electronics HW Set

24 Jul 2008 | Series | Contributor(s): Dragica Vasileska, Gerhard Klimeck