N = 1000 x_max = 5.0 x = np.linspace(-x_max, x_max, N) dx = x[1]-x[0] V = 0.5 * x**2 # harmonic potential example diag = 1.0/dx**2 + V off = -0.5/dx**2 * np.ones(N-1) H = diags([diag, off, off], [0, -1, 1]) vals, vecs = eigsh(H, k=6, which='SM') print(vals) # eigenenergies

Mathematical formulation of Heisenberg’s Uncertainty Principle and its physical applications (such as the non-existence of electrons in the nucleus). 2. The Schrödinger Wave Equation

with another popular title (like Griffiths or Zettili).

Physical significance of the wave function ( ), normalization conditions, and probability density.