Mushtaq Ali

Wavefunction evolution in a one-dimensional infinite square well is now predicted directly by a transformer, with probability normalization imposed as a hard architectural constraint on the output rather than a soft loss penalty. An unconstrained multilayer perceptron left total probability between 1.039418 and 1.045530, away from unity; the constrained model held the maximum probability deviation to 2.98×10⁻⁷ across ground, first-excited, Gaussian wavepacket and superposition initial states, with mean fidelity 0.999949. At matched spatial resolution, one forward pass takes roughly 0.0006 to 0.001 s, reaching a 22.35× speedup over sequential Crank–Nicolson at a 195-step horizon.

Wavefunction evolution in a one-dimensional infinite square well is now predicted directly by a transformer, with probability normalization imposed as a hard architectural constraint on the output rather than a soft loss penalty. An unconstrained multilayer perceptron left total probability between 1.039418 and 1.045530, away from unity; the constrained model held the maximum probability deviation to 2.98×10⁻⁷ across ground, first-excited, Gaussian wavepacket and superposition initial states, with mean fidelity 0.999949. At matched spatial resolution, one forward pass takes roughly 0.0006 to 0.001 s, reaching a 22.35× speedup over sequential Crank–Nicolson at a 195-step horizon.