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Schrodinger Equation - Example 4

In quantum mechanics, the Schrodinger equation is a mathematical equation that describes the change in quantum states of a physical system in terms of its quantum wave function. The wave function contains information about the probability amplitude of position, momentum, and other physical properties of a particle. The Schrödinger equation determines how the wave function changes with time—it expresses the quantum dynamics of a system. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.

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Marshall S.

University of Washington

Farnaz M.

Simon Fraser University

Jared E.

University of Winnipeg

Meghan M.

McMaster University

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Video Transcript

welcome to our fourth example video. Looking at Schrodinger's equation in this video, we're going to consider another potential well problem. But we're going to say that we have distinguished that the difference between E to and the one that is our second energy level and our first energy level is going to be equal to 4.2 e. B. And from this, we would like to determine what sort of well are electron is inside. That is to say, How long is it? What is the dimension in the What is the length of the dimension inputs? The electron is moving, so we we know this and we know we have e n is equal to age squared over eight l squared multiplied by m n squared, Um, and so I could plug those in. I know I have aged squared over eight l squared M times we have n squared, so that will be two squared minus eight squared over eight l squared m times one squared has to be equal to 4.2 e v. So what I need to do is I need to solve for l notice here I could pull out a factor of one over l squared, which would then allow me to say that l is going to be equal to We have h squared over eight AM times 4.2 e v multiplied by We have two squared minus one squared, and we have to take the square root of the entire thing. And this will be how we confined our length. You can go through and find for yourself that the units here are correct and you can type it in to find out what is the size of this potential? Well, given we have this energy difference now, this may seem like a strange problem, but it turns out that finding a difference between two energy levels those little easier than you might think.

RC
University of North Carolina at Chapel Hill
Top Physics 103 Educators
Marshall S.

University of Washington

Farnaz M.

Simon Fraser University

Jared E.

University of Winnipeg

Meghan M.

McMaster University