Physics
Quantum Mechanics 1
McGraw Hill
Pearson
Cengage
Houghton Mifflin Harcourt
John Wiley & Sons
Dummies (Wiley)
The cat is not dead.
Math background for quantum 1
From experiment to theory - Stern Gerlach
Math framework for quantum
Measurement and uncertainty
Schrodinger equation
Particle in a box
Angular momentum
Harmonic oscillator
Equations
\begin{equation}
F_z = \frac{\partial}{\partial z} (\boldsymbol{\mu} \cdot \textbf{B}) \tag{1.1}
\end{equation}
\begin{equation}
\mu = IA \tag{1.2}
\end{equation}
\begin{equation}
\boldsymbol{\mu} = g \frac{q}{2m} \textbf{S} \tag{1.3}
\end{equation}
\begin{equation}
S_z = \pm \frac{\hbar}{2} \tag{1.4}
\end{equation}
\begin{equation}
\hbar = 1.0546 \times 10^{-34} \: \textnormal{J/Hz} = 6.5821 \times 10^{-16} \: \textnormal{eV/Hz} \tag{1.5}
\end{equation}
\begin{equation}
\hat{ \textbf{i}} \cdot \hat{ \textbf{i}} = \hat{ \textbf{j}} \cdot \hat{ \textbf{j}} = \hat{ \textbf{k}} \cdot \hat{ \textbf{k}} = 1 \qquad \textnormal{(normalization)}
\end{equation}
\begin{equation}
\hat{ \textbf{i}} \cdot \hat{ \textbf{j}} = \hat{ \textbf{i}} \cdot \hat{ \textbf{k}} = \hat{ \textbf{j}} \cdot \hat{ \textbf{k}} = 0 \qquad \textnormal{(orthogonality)}
\end{equation}
\begin{equation}
\textnormal{A} = a_x \, \hat{ \textbf{i}} + a_y \, \hat{ \textbf{j}} + a_z \, \hat{ \textbf{k}} \qquad \textnormal{(completeness)}
\end{equation}
\begin{equation}
\ket{ \psi } = a \ket{+} + b \ket{-} \tag{1.6}
\end{equation}
\begin{equation}
\bra{ \psi } = a^* \bra{+} + b^* \bra{-}
\end{equation}
\begin{equation}
\left( \bra{bra} \right) \left( \ket{ket} \right) \tag{1.7}
\end{equation}
\begin{equation}
\left( \bra{+} \right) \left( \ket{-} \right) = \bra{+}- \rangle \tag{1.8}
\end{equation}
\begin{equation}
\bra{+}+ \rangle = \bra{-}- \rangle = 1 \qquad \textnormal{normalization}
\end{equation}
\begin{equation}
\bra{+}- \rangle = \bra{-}+ \rangle = 0 \qquad \textnormal{orthogonality}
\end{equation}
\begin{equation}
\ket{ \psi } = a \ket{+} + b \ket{-} \qquad \textnormal{completeness}
\end{equation}
\begin{equation}
\bra{-} \psi \rangle = \bra{-} \left(a \ket{+} + b \ket{-} \right)
\end{equation}
\begin{equation}
= \bra{-} a \ket{+} + \bra{-} b \ket{-}
\end{equation}
\begin{equation}
= a \bra{-} + \rangle + b \bra{-} - \rangle
\end{equation}
\begin{equation}
= b
\end{equation}
\begin{equation}
\bra{ \psi } - \rangle = \bra{+} a^* \ket{-} + \bra{-} b^* \ket{-}
\end{equation}
\begin{equation}
= a^* \bra{+} - \rangle + b^* \bra{-} - \rangle
\end{equation}
\begin{equation}
= b^*
\end{equation}
\begin{equation}
\bra{+} \psi \rangle = \bra{ \psi } + \rangle^* \tag{1.9}
\end{equation}
\begin{equation}
\bra{\theta} \psi \rangle = \bra{ \psi } \theta \rangle^* \tag{1.10}
\end{equation}
\begin{equation}
P_{ \pm } = | \bra{\pm} \psi \rangle | ^2 \tag{1.11}
\end{equation}