Using the normalization condition, show that the constant [tex]A[/tex] has the value [tex](\frac{m\omega_0}{\hbar\pi})^{1/4}[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

I know from text the text book that

[tex]\psi(x)=Ae^{-ax^2}[/tex]

where [tex]A[/tex] is the amplitdue and [tex]a=\frac{\sqrt{km}}{2\hbar}[/tex]

Here is my working:

Because the motion of the particle is confined to -A to +A, so the probability of finding the particle in the interval of -A to +A must be 1. Therefore the normalization condition is

[tex]\int_{-A}^{A}|\psi(x)^2| dx = 1[/tex]

[tex]A^2\int_{-A}^{A} e^{-2ax^2} dx = 1 [/tex]

Here's where I'm stuck, this equation cannot be solved via integration techniques, it can only be solved using by numerical methods. I only know the "trapezium rule" and the "Simpson's Rule", I tried both of methods but nothing came up. Does this problem require some other numerical methods or is my normalization condition incorrect?

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# Homework Help: Simple Harmonic(Quantum) Oscillator

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