Consider a particle of mass m in a finite square well with potential energy -Vo for a≤x≤+a where V (x)= 0 Note that a is a positive constant. otherwise, 2h2 Vo ma2 (a) Solve the TISE. You should find that there are two sets of eigenfunctions. For one set, each eigenfunction has the form Ale+ ₁(x)=C₁ cos la Alex for 2-a for a≤x≤ta for x+a, while for the other set, each eigenfunction has the form 2(x)= Aze+k D2 sin la for 2-a fora≤ x ≤+a -Age 511 where 2m E h for r+a, 2m (Vo-E) Note that {A1, C1, A2, D2) are constants to be determined. h (b) Show that Y -{ X tan X for the case of 1 (2) -X cot X for the case of 2(2), where X := la and Y = ka are dimensionless quantities. (c) How many bound states are there here? Find the allowed mechanical energies, expressing each one as a multiple of h²/(ma²).