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i. Find a mathematical description of the potential at the bottom of the well by scaling and shifting a

sine function to achieve the required shape. Illustrate this with a plot of your chosen function.

ii. Write down the perturbed Hamiltonian

With part (i) is this asking for a function that relates the sine wave to the potential. I know that the bottom of the well is in a shape such that it has the negative part of the sine curve as its base. I can't get an equation for the potential at the bottom of the well.

I have tried using sin((gamma + 1)*pi) where 0 < gamma < 1 but it doesn't seem to work through.

What should i do in order to find the function for the potential at the bottom of the well.

thanks in advance.