Using Schrodinger's equation, find the potential U(x) and energy E such that the given wave function is an eigenfunction (we can assume that at x = infinity there is 0 potential).
Can anyone provide the answer?
Can anyone provide the answer?
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Your equation is unreadable, so don't be surprised if you don't get many answers!
I don't know if I could solve it anyway as my maths is very rusty. But I would start by finding d²ψ/dx². Then substitute this into the time-independent equation:
-[h_bar²/(2m)]d²ψ/dx² + V(x)ψ(x) = Eψ(x)
Simplify the resulting equation then inspect it to look for solutions giving V(infinity) = 0. (Solutions could be simple functions such as V = k/x or V = k/x²).
I don't know if I could solve it anyway as my maths is very rusty. But I would start by finding d²ψ/dx². Then substitute this into the time-independent equation:
-[h_bar²/(2m)]d²ψ/dx² + V(x)ψ(x) = Eψ(x)
Simplify the resulting equation then inspect it to look for solutions giving V(infinity) = 0. (Solutions could be simple functions such as V = k/x or V = k/x²).