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A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state. DO NOT USE THIS TAG for classical waves.

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How to find the wavefunction that solves an infinite square well with a delta function well ...

Then for $0<x<L/2$ we have $$\psi(x)=C\sinh(\kappa x)$$ and for $L/2<x<L$ we have $$\psi(x)=-C\sinh(\kappa(x-L))$$ Now, applying the calculation for the discontinuity in the derivative of the wavefunction … even possible to have a solution for $E=0$: For $0<x<L/2$ we have: $$\psi(x) = Cx$$ And for $L/2 < x<L$ we have: $$\psi(x)= C(L-x)$$ The dirac potential allows a discontinuity of the derivative of the wavefunction
Hubert van Luytelaar's user avatar