# Visualize the wave functions of a quantum well. 
# This is a realization (with adaptations and corrections) of the application note alpaca_22 from https://analogparadigm.com.
# Schrödinger's equation is here to psi'' = -(U0+epsilon)*psi

coefficient(1): +1 -> l # left boundary of quantum well
coefficient(2): -1 -> r # right boundary of quantum well
coefficient(3): +1 -> +U0 # depth of quantum well
coefficient(4): +1 -> epsilon # energy of system
coefficient(5): +1 -> psi'0
coefficient(6): -1 -> -psi0
coefficient(8): -1 -> slowing_t # slowing down t

# First, generating a time ramp from -1 to +1
iintegrate slowing_t -> t
  IC: +1

# Defining the boundaries of the quantum well
compare t, l -> well_left
  GT0: -U0   # LT0 is open, thus =0
compare t, r -> well
  LT0: well_left # GT0 is open, thus =0

# adding epsilon to the well and calculating the wave function
isum epsilon, well -> -(well+epsilon)
multiply -(well+epsilon), psi -> -(well+epsilon)*psi
iintegrate -(well+epsilon)*psi -> -psi' # input is psi''
  IC: psi'0
iintegrate -psi' -> psi
  IC: -psi0
  
multiply psi, psi -> psi^2
invert well -> -well

output(x): psi
output(y): psi^2
output(z): -well
output(u): t      # also used as trigger