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Dr. Walther | Dr. Walther | ||
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== Table of Contents == | == Table of Contents == | ||
1. Introduction | 1. Introduction | ||
| − | 2. Applications and Further Readings | + | 2. The Wavefunction |
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| + | 3. Derivation | ||
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| + | 4. Particle-in-a-box | ||
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| + | 5. Applications and Further Readings | ||
== Introduction == | == Introduction == | ||
| + | <center><math> \hat H \psi = E \psi</math></center> | ||
| + | First postulated in 1925 by its namesake discoverer, Erwin Schrodinger, the Schrodinger equation is used to describe the wavefunction of particles – that is, an equation that unifies the wave and particle nature of the energy of matter. In its most simple form, it is expressed as a partial differential equation between its energy, representing the wave characteristic, and the Hamiltonian, describing its particle nature. The equation became the foundation for the field known today as quantum mechanics. Although expressible in many different forms, in this paper we limit our scope to perhaps the most famous and simple systems, the particle-in-a-box. We will then examine applications of the Schrodinger equation in modeling of the hydrogen atom and quantum tunneling. | ||
[[Category:MA271Fall2020Walther]] | [[Category:MA271Fall2020Walther]] | ||
Revision as of 06:07, 6 December 2020
Schrödinger Equation
Varun Chheda
Dr. Walther
Table of Contents
1. Introduction
2. The Wavefunction
3. Derivation
4. Particle-in-a-box
5. Applications and Further Readings
Introduction
First postulated in 1925 by its namesake discoverer, Erwin Schrodinger, the Schrodinger equation is used to describe the wavefunction of particles – that is, an equation that unifies the wave and particle nature of the energy of matter. In its most simple form, it is expressed as a partial differential equation between its energy, representing the wave characteristic, and the Hamiltonian, describing its particle nature. The equation became the foundation for the field known today as quantum mechanics. Although expressible in many different forms, in this paper we limit our scope to perhaps the most famous and simple systems, the particle-in-a-box. We will then examine applications of the Schrodinger equation in modeling of the hydrogen atom and quantum tunneling.
