I'm looking for a QM book structured similar to Norvig LISP books, ie following a demonstrative didactic method, by building computational implementations of toy models demonstrating various aspects of QM (not just QC), toy models of resonator, particle in a box, etc

The problem is that after the basics of QM, there were literally hundreds of papers by dozens of important scientists developing the subsequent theory. And you can no longer teach the subject in a linear historical fashion.

[1] https://www.cengage.com/c/modern-physics-3e-serway-moses-moy...

[1] https://press.princeton.edu/books/paperback/9780691033273/qe...

If you want something that's more focused throughout on the historical progression, a classic book is Jammer's Conceptual Development of Quantum Mechanics, but it assumes you're already familiar with quantum and statistical mechanics.

If you like videos, the physicist Jorge Diaz has excellent videos accessibly detailing the experimental and theoretical history https://www.youtube.com/@jkzero/playlists

In this interview he goes over pretty much exactly what you mentioned (and a lot more):

https://www.youtube.com/watch?v=7oWip00iXbo

https://global.oup.com/academic/product/the-quantum-cookbook...

The Quantum Cookbook

Mathematical Recipes for the Foundations of Quantum Mechanics

Jim Baggott

1:Planck's Derivation of E = hn: The Quantisation of Energy

2:Einstein's Derivation of E = mc2: The Equivalence of Mass and Energy

3:Bohr's Derivation of the Rydberg Formula: Quantum Numbers and Quantum Jumps

4:De Broglie's Derivation of / = h/p: Wave-particle Duality

5:Schrödinger's Derivation of the Wave Equation: Quantisation as an Eigenvalue Problem

6:Born's Interpretation of the Wavefunction: Quantum Probability

7:Heisenberg, Bohr, Robertson, and the Uncertainty Principle : The Interpretation of Quantum Uncertainty

8:Heisenberg's Derivation of the Pauli Exclusion Principle: The Stability of Matter and the Periodic Table

9:Dirac's Derivation of the Relativistic Wave Equation: Electron Spin and Antimatter

10:Dirac, Von Neumann, and the Derivation of the Quantum Formalism: State Vectors in Hilbert Space

11:Von Neumann and the Problem of Quantum Measurement: The 'Collapse of the Wavefunction'

12:Einstein, Bohm, Bell, and the Derivation of Bell's Inequality: Entanglement and Quantum Non-locality

Not a book per se, but if interested in videos, run, don't walk to check out Jorge Diaz's channel (see https://www.youtube.com/watch?v=MCJl3-pHGuU for example). It is just what you're asking for.

Another underrated channel for historical chemistry/physics fans: Marb's Lab at https://www.youtube.com/@Marbslab

You can solve any problem by using only the Lagrangian, there is really no need for the Hamiltonian, which also has the disadvantage of not being relativistically invariant, like the Lagrangian.

Also the name of "Hamiltonian" is somewhat misused. The most important contribution of Hamilton has been the definition of Hamilton's integral, i.e. the integral over time of the Lagrangian. That is an extremely important function and it would have deserved better the name of "Hamiltonian", than the less important Hamiltonian, which also was not introduced for the first time by Hamilton.

How to transform the system of equations of Lagrange to the "Hamiltonian" form had already been described by Poisson, and then by Cauchy, the latter using a form exactly equivalent to that presented later by Hamilton.

The notation H for the Hamiltonian has nothing to do with the name of Hamilton. Lagrange had used H for this quantity in 1811, without giving any meaning to the letter, then Hamilton in 1834 has reused the notations of Lagrange, adding "function S" for Hamilton's integral, also without giving any meanings to the letters.