Question

m, leaving us with: hay = E(x)ip(x) 2m dx2

Answer 1

Bound state problems: - In classical mech, E = -ve then state will be bound state. But in Q middot M, if E = -ve then state may but it is not necessary. In P middot M to find weather the state is bound or not, we use time independent schr eqn If particle is completely free then the no force on particle (i.e. No restriction) for free particle, F = 0 - nabla v = 0 dv/dx = 0 rightdoublearrow v = 0 v = v_0 P middot E is not a free of position 4 (it is 0 for free particle, or energy is of position. Schrodinger eqn for free particle H psi = E psi - hwithstroke^2/2 d^2/dx^2 psi = E psi d^2 psi/dx^2 + 2m E/hwithstroke^2 psi = 0 d^2 psi/dx^2 + k^2 psi = 0 solution m^2 + k^2 = 0 roots m = plusminus ik psi (x) = Ae^ikx + Be^-ikx \r\n d^2 psi/dx^2 + 2mE/hwithstroke^2 psi = 0 d^2