From: Permondes Date: Thu, 18 Jul 2024 09:41:31 +0000 (+0200) Subject: Quantum Well X-Git-Url: https://permondes.de/gitweb/Analog_Engine.git/commitdiff_plain/8f52e908448be35d3814a396e1cd4867b41faf94 Quantum Well Application: quantum well --- diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt index 96723b6..bc0ea21 100644 Binary files a/Analog Engine Example Applications.odt and b/Analog Engine Example Applications.odt differ diff --git a/scripts/alpaca22 Quantum Well.LACE b/scripts/alpaca22 Quantum Well.LACE new file mode 100644 index 0000000..07b4ee8 --- /dev/null +++ b/scripts/alpaca22 Quantum Well.LACE @@ -0,0 +1,37 @@ +# 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