permondes.de Git - Analog_Engine.git/blob - 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

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

13 # First, generating a time ramp from -1 to +1

14 iintegrate slowing_t -> t

15 IC: +1

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

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

31 multiply psi, psi -> psi^2

32 invert well -> -well

34 output(x): psi

35 output(y): psi^2

36 output(z): -well

37 output(u): t # also used as trigger