dyn said:Antisymmetric wavefunction would have the form of sine so 1st derivative would be cos(0) =1 , 2nd derivative would be sin(0)=0. I can't see how that helps and the same would happen for the 1st and 3rd excited states as well
A delta function potential is a mathematical concept used in physics and mathematics to describe a localized potential energy that is infinitely strong at a single point and zero everywhere else. It is represented by the Dirac delta function, which is zero everywhere except at the point of interest where it is infinite.
Delta function potentials are commonly used in quantum mechanics to model point-like interactions between particles. They can also be used in classical mechanics to model point-like forces acting on a system. In both cases, the delta function potential is used to represent a strong, localized interaction at a specific point.
One of the main properties of a delta function potential is that it is infinitely strong at the point of interest and zero everywhere else. It is also an odd function, meaning that it is symmetric about the origin and its integral over the entire real line is equal to 1.
A delta function potential is represented by the Dirac delta function, which is denoted as δ(x). It is defined as zero for all values of x except at x = 0, where it is infinite. It is also important to note that the Dirac delta function is not a proper function in the traditional sense, but rather a distribution or generalized function.
Delta function potentials can be observed in many physical systems, such as the interaction between an electron and a nucleus in an atom, where the electron experiences a strong, localized potential at the nucleus. They can also be used to model the force between two particles in a molecule, where the particles are treated as point-like objects. Other examples include the interaction between a particle and a boundary surface, and the behavior of electrons in a crystal lattice.