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  Square Well Energies: (atomic units are "mostly" used)
  Default Parameters are for:
      Quantum Mechanics Homework Problem

          Depth of Well = Vo = 13.6 eV = 0.4997908 Eh
          Width of well = L = 2 nm = 37.7929 Bohr
          Mass of electron = m_e = 1 au
          hbar = 1 au

     We use the reduced equation 10 from Eur. J. Phys. 13, 21-25 (1992):
         f(t) = t/s - sin(0.5*n*pi - t)  (good for even or odd parity)  
         fp(t) = 1/s + cos(0.5*n*pi -t)  (df/dt)
     The even-parity states are n=1,3,5,...
     while the odd-parity states are n=2,4,6,...
     The maximum number of bound states is obtained from
         n_max = int(2*s/pi) + 1
     The initial guess for each state t_n0 is
         t_n0 = n*pi/2
     Here s^2 is the strength parameter,
               s**2 = 0.5*m*Vo*(L/hbar)**2,
     and t is defined as
               t**2 = 0.5*m*E_n*(L/hbar)**2.
     The ionization energy epsilon_n = Vo - E_n and
     E_n is the eigenvalue for the nth bound state of the
     well. 

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