# How to plot a function with several constants using Wolfram Mathematica

How can I plot this probability density function using Wolfram Mathematica Keeping the constants the same.

ψ*ψ= A^2 (x^2)exp(-2a(mx^2/h)) ; where m,a,A,and h are constants and I want the graph in terms of them.

I tried: Plot[A^2 *(x^2)*exp(-2a(mx^2/h)),{x,-1000,1000}]

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vela
Staff Emeritus
Homework Helper
You can't.

How can I plot this probability density function using Wolfram Mathematica Keeping the constants the same.

ψ*ψ= A^2 (x^2)exp(-2a(mx^2/h)) ; where m,a,A,and h are constants and I want the graph in terms of them.

I tried: Plot[A^2 *(x^2)*exp(-2a(mx^2/h)),{x,-1000,1000}]
I would say you can't do that since Wolfram Alpha assumes that these terms are variables. Hence, there is no approach for this. You could just substitute the constants with any values and then, check the graph. You just have a graph; that doesn't guaranteed the exact graph you should expect. You will need to substitute random values!

I may be wrong. I am just assuming that is true.

vela
Staff Emeritus
Homework Helper
You should be able to solve for A in terms of a, m, and h by requiring the wave function be normalized. That'll get rid of one constant.

What you want to do is come up with some combination of the constants that is a characteristic length in the problem. In this case, your wave function is
$$\psi(x) = A x e^{-\frac{ma}{\hbar}x^2}.$$ The argument of the exponential has to be unitless, and if you check the units, you'll indeed find that the combination ##ma/\hbar## has units of 1/length2. A natural choice for your length scale would therefore be ##\alpha=\sqrt{\hbar/ma}##. Now if you change variables from ##x## to ##x/\alpha##, you'll find that all of the constants will be gone. Once you have the density in that form, you can plot it using Mathematica.

phyzguy