QM - 103 Particle in a Finite Square Well -- Bound States

Every attractive potential can be represented by a potential well. A square potential well is easiest to solve the Schroedinger equation in one dimension, primarily because the boundary conditions are at a fixed value of xm corresponding to the (half) width of the square well. This also yields solutions for energy levels, discrete. Recall, classically we could have any energy value, but boundary conditions impose conditions such that only certain energy levels are allowed. No matter how thin or how shallow the potential well is, in this case, there will ALWAYS be one bound state. Since the potentail well chosen had a symmetry about x = 0, the solutions also had the symmetry. These are divided into even parity and odd parity. I did not solve each step here. The treatment that I follow is from the QM book by Matthews and Venkatesan. Follow any book you like, and in case there are those who is unable to solve the few unsolved steps of the book, please feel free to write here. I shall send you the solution. The starting of this video is a little abrupt -- technical glitch. I did not want to re record it -- please bear with it. #physicswithprof