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## Homework Statement

Please I am just going to list the question then show my solving, It is a physics question but I need help on integration, on parts of the question, thank you

quesiton:

A particle in the infinite square well, (i.e [tex] V(x) = \left{ \begin{array}{ccc} 0 & \textrm({ if 0 <= x <= a} \\ \infty & otherwise \end{array}\right [/tex]

has the initial wave function

[tex] \Psi(x,0) = Asin^3(\frac{\pi x}{a} \textrm{ for (0<=x<=a) } [/tex]

Determine A, find [tex] \Psi(x,t) \textrm{ and calculate <x> as a function of time, what is the expectation value of the energy? (hint: sin^n \theta and cos^n \theta can be reducted by repeated application of trigonometric sum formulas, to linear combinatiosn of sin(m\theta) and cos(m\theta), with m = 0,1,2....n }

[/tex]

## Homework Equations

[tex] 1 = \int_{-\infty}^{\infty} |\Psi(x,0)|^2 dx [/tex]

## The Attempt at a Solution

My attempt, well first I normalize it,

so the solution to the question is,

[tex] \int_0^a |A sin^3(\frac{\pi x}{a}|^2 = 1 [/tex]

now this brings up something I do not know how to solve,

since the sin would go to the ^6 power

I was told by my course instructor that there are many ways to solve integrals of this type,

and the question states Sin^n theta can be reduced by repeated application of the trigonometric sum formulas, to linear combinations of sin

so I have to use some trigonometric identities to solve/simplify the integral basically

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