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}