Explanation Given: If ψ is a function of x and V = V ( r ) Replace x by α x α = m ω h Concept used: If ψ is a function of x and V = 0 This is a one dimentional harmonic oscillator First separate variables in the general equation ψ ¯ = ψ ( x , y , z ) T ( t ) − h 2 2 m ψ ∇ 2 ψ + V = i h 1 T d T d t = E Where E is separate constant Integrating the time equation T = e i E t / h Calculation: If ψ is a function of x and V = 0 This is a one dimentional harmonic oscillator First separate variables in the general equation ψ ¯ = ψ ( x , y , z ) T ( t ) − h 2 2 m ψ ∇ 2 ψ + V = i h 1 T d T d t = E Where E is separate constant Integrating the time equation T = e i E t / h The space equation is − h 2 2 m ∇ 2 ψ + V ψ = E ψ Time independent schrodinger equation For the one dimentionaL − h

Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Chapter 13.7, Problem 18P

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The steady state temperature distribution inside a sphere of radius 1 and outer radius 2 when the surface temperatures

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Chapter 13.7, Problem 17P

Chapter 13.7, Problem 19P

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Chapter 13 Solutions

Mathematical Methods in the Physical Sciences

Ch. 13.1 - Assume from electrostatics the equations E=/0 and...Ch. 13.1 - Show that the expression u=sin(xvt) describing a...Ch. 13.1 - Assume from electrodynamics the following...Ch. 13.1 - Obtain the heat flow equation (1.3) as follows:...Ch. 13.2 - After you find the series solution of a problem,...Ch. 13.2 - T=0,0x10,100,10x20. Solve the semi-infinite plate...Ch. 13.2 - Solve the semi-infinite plate problem if the...Ch. 13.2 - Solve the semi-infinite plate problem if the...Ch. 13.2 - Show that the solutions of (2.5) can also be...Ch. 13.2 - Show that the series in (2.12) can be summed to...

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The steady state temperature distribution inside a sphere of radius 1 and outer radius 2 when the surface temperatures

Solution Summary: The author calculates the steady state temperature distribution inside a sphere of radius 1 and outer radius 2 when the surface temperatures are constant.

To find: The steady state temperature distribution inside a sphere of radius 1 and outer radius 2 when the surface temperatures

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Chapter 13 Solutions

To find:

The steady state temperature distribution inside a sphere of radius 1 and outer radius 2 when the surface temperatures