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## Quantum Bound States Exercise

1. Purdue University 2. Arizona State University

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#### Abstract

Exercise Background

Quantum-mechanical systems (structures, devices) can be separated into open systems and closed systems. Open systems are characterized with propagating or current carrying states. Closed (or bound) systems are described with localized wave-functions. One such system is a triangular potential well in MOS capacitors; another one is rectangular quantum well in heterostructure devices. In addition to this, every observable in Quantum Mechanics (like position, momentum, energy) is represented by an operator, the expectation values of which describes the mean or the mean-square location of the particle in either position space or momentum space. Position and momentum operators in a way are special operators because they do not commute, which in physical terms means that one cannot simultaneously determine the position and the momentum of the particle so that the concept of trajectory is ill-defined.

Exercise Objectives

You will be aware of the following items by successfully attempting the questions given in this assignment:

1. Learn how to work with the position and the momentum operators used in Quantum
Mechanics.

2. Making use of the Bound States Calculation Lab will help you understand about the
spatial spread of the wave-functions and the eigen energies in the well and will allow
you to compare to infinite square well results.

#### Cite this work

Researchers should cite this work as follows:

• Gerhard Klimeck; Parijat Sengupta; Dragica Vasileska (2010), "Quantum Bound States Exercise," https://nanohub.org/resources/9191.

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