Deriving the 3D Wave Equation: A Comprehensive Explanation

Tuneman
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I would like to know how to derive the wave equation for a 3 dimensional case, I was looking it up on wikipedia, and their explination wasn't very comprehensive, I was wondering if anyone knew of any other website that would be able to let me fullly understand it.

Edit: not the shrodinger wave equation, but general case of a wave.
 
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Not sure what you mean by 3 dimensional case but I think it is just a definition. If you see an equation of the form U_tt = U_xx + U_yy + U_zz we choose to call it the wave equation in three dimensions.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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