Add variational neural network solver - #43

Summary

• add VariationalNeuralNetwork with the VNN abbreviation
• support both a standard Lux network built from architecture and arbitrary user-supplied Lux models
• evaluate and normalize trial wavefunctions using the finite-difference Hamiltonian, radial Jacobian, and Rayleigh quotient
• support training continuation through Lux parameters, states, and optimizer state
• add validation, tests, documentation, and dependency declarations

Why

This implements the neural-network trial wavefunction proof of concept proposed in #33 while keeping the FDM discretization as the shared numerical backend. The convenience API covers the common case, while the explicit-model API allows users to experiment with custom Lux architectures and trial envelopes.

User impact

Users can now write either:

result = solve(H, VNN(...))

or pass an arbitrary Lux model:

result = solve(H, model, VNN(...); trial=(r, value) -> exp(-r) * value)

The result includes the variational energy, normalized grid wavefunction, callable wavefunction, training history, Lux state, and optimizer state.

Validation

• Julia 1.10.10: full package test suite passed (344/344)
• Julia 1.7.3: targeted VNN compatibility tests passed
• Documenter: VNN page built successfully with executable examples
• git diff --check passed

The full local documentation site was not completed because the shared host Julia cache repeatedly stalled while precompiling CairoMakie; the VNN page itself builds cleanly without warnings.

Closes #33

This pull request was developed with assistance from Codex using GPT-5.6 Sol with High reasoning effort.