scripts/alpaca22 Quantum Well.LACE

   1 # Visualize the wave functions of a quantum well.
   2 # This is a realization (with adaptations and corrections) of the application note alpaca_22 from https://analogparadigm.com.
   3 # Schrödinger's equation is here to psi'' = -(U0+epsilon)*psi
   4
   5 coefficient(1): +1 -> l # left boundary of quantum well
   6 coefficient(2): -1 -> r # right boundary of quantum well
   7 coefficient(3): +1 -> +U0 # depth of quantum well
   8 coefficient(4): +1 -> epsilon # energy of system
   9 coefficient(5): +1 -> psi'0
  10 coefficient(6): -1 -> -psi0
  11 coefficient(8): -1 -> slowing_t # slowing down t
  12
  13 # First, generating a time ramp from -1 to +1
  14 iintegrate slowing_t -> t
  15   IC: +1
  16
  17 # Defining the boundaries of the quantum well
  18 compare t, l -> well_left
  19   GT0: -U0   # LT0 is open, thus =0
  20 compare t, r -> well
  21   LT0: well_left # GT0 is open, thus =0
  22
  23 # adding epsilon to the well and calculating the wave function
  24 isum epsilon, well -> -(well+epsilon)
  25 multiply -(well+epsilon), psi -> -(well+epsilon)*psi
  26 iintegrate -(well+epsilon)*psi -> -psi' # input is psi''
  27   IC: psi'0
  28 iintegrate -psi' -> psi
  29   IC: -psi0
  30
  31 multiply psi, psi -> psi^2
  32 invert well -> -well
  33
  34 output(x): psi
  35 output(y): psi^2
  36 output(z): -well
  37 output(u): t      # also used as trigger