Notation and colours

The book follows the notation of Centini’s whiteboards throughout. Where Griffiths’ Introduction to Quantum Mechanics and Zettili’s Quantum Mechanics, the books the exercises come from, differ, the last column says how.

Symbols

Symbol	Meaning	Griffiths, Zettili
$Real c$ , $Imag c$	real and imaginary part	$Re$ , $Im$
$c^{*}$ , $∣ c ∣$ , $θ$	conjugate, modulus, phase of $c = ∣ c ∣ e^{i θ}$	same; $ϕ$ for the phase
$arctg$ , $tg$ , $ctg$	arctangent, tangent, cotangent	$tan^{- 1}$ , $tan$ , $cot$
$φ_{0}$	initial phase of a wave	$ϕ$ , $δ$
$\overset{r}{ˉ}$ , $\overset{p}{ˉ}$ , $\overset{ˉ}{L}$	vectors, with a bar	$r$ , $r$
$\hat{A}$	an operator	same
$\hat{A}^{+}$	Hermitian adjoint	$\hat{A}^{†}$
$u_{n}$ , $a_{n}$	eigenfunctions of $\hat{A}$ and its eigenvalues, $\hat{A} u_{n} = a_{n} u_{n}$	$ψ_{n}$ , $f_{n}$ / $ϕ_{n}$ , $a_{n}$
$b_{n}$	components of the state, $b_{n} = ⟨ u_{n} ∣ ψ ⟩$	$c_{n}$
$⟨ f ∣ g ⟩$	$\int f^{*} g d^{3} r$	same
$⟨ \hat{A} ⟩$	expectation value, $⟨ ψ ∣ \hat{A} ∣ ψ ⟩$	$⟨ A ⟩$
$Δ A$	standard deviation, $⟨ \hat{A}^{2} ⟩ - ⟨ \hat{A} ⟩^{2}$	$σ_{A}$
$[\hat{A}, \hat{B}]$	commutator, $\hat{A} \hat{B} - \hat{B} \hat{A}$	same
$U (x)$ , $U_{0}$	potential energy, its height or depth	$V (x)$ , $V_{0}$
$k_{0}$ , $κ$	wavenumber where $E > U$ , decay constant where $E < U$	$k$ , $κ$ or $l$ , $κ$
$a$	the well’s half-width (finite well), or width (infinite well)	$a$ width; Griffiths’ finite well has half-width $a$
$\overset{a}{^}$ , $\overset{a}{^}^{+}$	ladder operators of the oscillator	$\overset{a}{^}_{-}$ , $\overset{a}{^}_{+}$
$\overset{σ}{^}_{x}, \overset{σ}{^}_{y}, \overset{σ}{^}_{z}$	Pauli matrices, $\hat{S}_{i} = \frac{ℏ}{2} \overset{σ}{^}_{i}$	same
$∣ + ⟩$ , $∣ - ⟩$	spin up and down along $z$	$χ_{+}$ , $χ_{-}$ / $∣ ↑ ⟩$ , $∣ ↓ ⟩$
$∣ j, m ⟩$	common eigenstate of $\hat{J}^{2}$ and $\hat{J}_{z}$	same
$\hat{J}_{\pm}$	raising and lowering operators, $\hat{J}_{x} \pm i \hat{J}_{y}$	same
$Y_{ℓ}^{m}$	spherical harmonics, Condon–Shortley phase	same
$\hat{P}_{12}$	exchange operator	$\hat{P}$
$e_{n}^{2}$	$e^{2} /4 π ε_{0}$	$e^{2} /4 π ϵ_{0}$ / $e^{2}$ in Gaussian units
$a_{0}^{'}$ , $μ$	Bohr radius with the reduced mass, the reduced mass	$a$ , $m$

Units in the demos

The demos use an electron, energies in eV and lengths in nm: $ℏ^{2} /2 m = 0.0381$ eV nm². A 1 nm infinite well then has $E_{1} = 0.376$ eV.

Colours

Colours carry meaning, and the same colour means the same thing in the text and in the demos, in both themes.

	Colour	Used for
$u_{1}$ , $u_{2}$ , $u_{3}$	red, green, blue	the family $n = 1, 2, 3$ : eigenstates, their levels, their components
$ψ$	violet	the state, and $∣ ψ ∣^{2}$ shaded
$\hat{A} ψ$	darker violet	what an operator makes of it
$a$	orange	the eigenvalue or eigenvector being looked for, a mean and its spread
$Real$ , $Imag$	teal, pink	real and imaginary parts
$U$	grey	the potential

Marks

Essential: one of the few definitions everything else is built on (Index of terms).
beyond the boards: added for this book: a proof the boards skip, an example, a picture, a result they state without deriving. Everything unmarked is on Centini’s whiteboards, this year’s or 2024/25’s.
Proofs, solutions and asides are folded; click to open them. A link with a dotted underline opens what it names in place; click it again to close.