Particle in a Box Problem
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Derivation of the Schrödinger equation
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Derivation of the Schrödinger equation
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Derivation of the Schrödinger equation
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Derivation of the Schrödinger equation
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Derivation of the Schrödinger equation
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Derivation of the Schrödinger equation
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Solution to the Schrödinger Equation
The solutions to the Schrödinger equation are called wave functions. A wave function gives a complete description of any system.
The time-independent Schrödinger equation can be solved analytically only in a few special cases such as:
In this next section we will discuss the solution of the Schrödinger equation for particle in a box. The remaining cases will be discussed later throughout the course.
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Particle in a One-Dimensional Box
The potential energy out side this space is set to infinity. Now the conditions of the potential energy of the particle are summarized as
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
Energy and wave function of a particle in a box
For a particle moving in a one dimensional box, we have shown that
and
We noticed from the graph that:
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
Correspondence principle
The probability distribution of a particle in a box.
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Particle in a One-Dimensional Box
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Particle in a One-Dimensional Box
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Postulates of Quantum Mechanics
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