Use this page as the chapter's final map. The point is not to memorize a sequence of names, but to connect each classical failure with the quantum rule that repairs it.
The central lesson is that old quantum physics finds the correct constraints before it has the correct language. Spectra, photons, matter waves and action quantization all point to the same destination: allowed states should be obtained from wave equations, boundary conditions and eigenvalues.
The chapter is best read as a chain of constraints, not as a loose list of discoveries. Each experiment removes one classical freedom and replaces it with a quantum condition.
| Classical expectation | Experimental pressure | Quantum move |
|---|---|---|
| Radiation can exchange any energy | Black-body spectrum stays finite | Energy packets \(E=hf\) |
| Light is only a wave | Photoelectrons need a threshold frequency | Photons with energy \(hf\) |
| Atomic orbits are arbitrary | Hydrogen emits discrete lines | Stationary states and transitions |
| Particles have no wavelength | Electrons diffract | Matter waves \(\lambda=h/p\) |
The sequence matters: Planck introduces energy packets, Einstein gives them experimental force, Bohr uses discrete energies to explain spectra, and de Broglie turns quantization into a wave condition.
| Topic | Central information | Key relation | What to remember |
|---|---|---|---|
| Hydrogen spectra | Lines are not continuous | \(1/\lambda=R(1/n^2-1/m^2)\) | Integers appear before the theory explains them |
| Black-body radiation | High-frequency modes are suppressed | \(\langle\epsilon\rangle=hf/(e^{hf/k_BT}-1)\) | \(h\) sets the energy scale |
| Photoelectric effect | Frequency controls electron energy | \(eV_c=hf-W\) | Intensity changes current, not the threshold |
| Bohr model | Allowed states explain spectral lines | \(L=n\hbar,\ E_n=-E_0/n^2\) | Useful model, but postulated rules |
| de Broglie | Particles carry wavelength | \(\lambda=h/p\) | Quantization becomes a wave condition |
| SCQR | Closed classical cycles select states | \(\oint p_i\,dq_i=n_i h\) | Bridge from orbits to boundary conditions |
These results point in the same direction. The next theory must handle waves, boundary conditions, discrete energies and probabilistic measurement in a single framework.
Old quantum physics succeeds when it identifies the right constraint, but it often has to impose that constraint by hand. Bohr postulates stationary states; SCQR postulates action quantization; de Broglie suggests waves but does not yet provide the equation that those waves obey.
Chapter 2 supplies the missing language: a state becomes a wave function, allowed energies become eigenvalues, and boundary conditions become part of a systematic calculation.
This page is designed to support short guided exercises on: A compact conceptual summary of the ideas that prepare the transition to Schrödinger's equation.
Use these anchors to design compact exercises. The exercise should be answerable from this page plus standard algebra, while longer derivations, full worked examples and broader context should point back to the original book.