Wave equation separation of variables
[DOC File]Chapter 12
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There are boundary value problems involving the wave equation for which separation of variables does not lead to the solution. This can occur because of the form of the wave equation (for example, there may be an external forcing term), or because of the form of the boundary conditions.
[DOC File]LECTURE 3 - Hope College
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Fundamental Equation of Quantum Chemistry. Schrodinger (1926): If particles possess wave-like properties, then there exists a wave equation which governs their behavior. Start with 1-D classical wave equation. Assume that the spatial solution is independent of time, i.e. separation of variables. then. Assumptions: 1) Classical wave equation
[DOC File]California State University, Northridge
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Find the solution to the wave equation in r and θ coordinates, using the steps outlined in the problem. The radial wave equation in two space dimensions (r and ) can be written as follows. [1] Substituting u = F(r,θ)G(t) gives the following separation of variables result. [2] Dividing by F(r,θ)G(t) gives the initial separation…
[DOC File]Ya’ gotta’ learn it all
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Wave equation: u = 0 on bd(M) Solution by separation of variables: u(x,t) = f(t)g(x), g = 0 on bd(M) This implies g must be an eigenfunction of ( - the eigenvalues determine the frequencies of vibration: So the eigenvalues determine the frequencies (overtones) the drum can produce. PROBLEM: Does the sequence of (’s determine the drum?
[DOC File]Review of Linear Wave Theory
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The linear solution for the potential of a periodic wave train can be derived using the method of separation of variables, and the corresponding solution for wave elevation can be obtained using Equation …
[DOC File]California State University, Northridge
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The solution of the wave equation by separation of variables proceeds in a manner similar to the solution of other partial differential equations. We postulate a solution that is the product of two functions, X(x) a function of x only and T(t) a function of time only. With this assumption, our solution becomes. u(x,t) = X(x)T(t) [29]
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