$N$: total lattice positions, $E_v/E_p$: energy to form defect.

Disturbed region between two perfect crystal parts.
Arise from growth accidents, thermal/external stresses.
Edge Dislocation: Extra half-plane of atoms inserted.
- Positive ('$\perp$') if extra plane is above slip plane, negative ('$\top$') if below.
Screw Dislocation: Displacement of atoms forming a spiral ramp around the dislocation line.
Burger's Vector ($b$): Quantifies the direction and magnitude of lattice distortion.
- For edge dislocation, $b$ is perpendicular to dislocation line.
- For screw dislocation, $b$ is parallel to dislocation line.

Dual Nature of Matter: Like light, matter (particles) also exhibits both wave and particle nature.
Matter Waves: Waves associated with material particles in motion.
De Broglie Wavelength: $\lambda = \frac{h}{p} = \frac{h}{mv}$
$h$: Planck's constant, $p$: momentum, $m$: mass, $v$: velocity.

In terms of Kinetic Energy ($E$): $\lambda = \frac{h}{\sqrt{2mE}}$
In terms of Voltage ($V$) for charged particle $q$: $\lambda = \frac{h}{\sqrt{2mqV}}$
- For electron: $\lambda = \frac{12.24}{\sqrt{V}} \text{ Å}$
In terms of Temperature ($T$): $\lambda = \frac{h}{\sqrt{3mk_BT}}$
$k_B$: Boltzmann constant.

Variable quantity associated with a moving particle at $(x,y,z,t)$.
$\Psi = \Psi_0 e^{-i\omega t}$ or $\Psi(x,y,z,t) = \Psi_0 e^{-i(\omega t - kx)}$.
Complex quantity, no direct physical meaning.
$|\Psi|^2 = \Psi\Psi^*$ is real and positive, representing probability density (probability of finding particle per unit volume).
Probability $P = \iiint |\Psi|^2 d\Gamma$. ($0 \le P \le 1$)
Properties: Single-valued, finite, continuous, analytical (continuous first derivative), vanishes at boundaries.
Normalized Wave Function: If $\iiint |\Psi|^2 d\Gamma = 1$.

Fundamental equations of quantum physics describing particle behavior.
Based on classical wave equation, de Broglie hypothesis, and conservation of energy.
Momentum Operator: $\hat{p} = -i\hbar \frac{\partial}{\partial x}$
Energy Operator: $\hat{E} = i\hbar \frac{\partial}{\partial t}$
$\hbar = h/2\pi$.

In 1D: $-\frac{\hbar^2}{2m} \frac{\partial^2\Psi}{\partial x^2} + V\Psi = i\hbar \frac{\partial\Psi}{\partial t}$
In 3D: $-\frac{\hbar^2}{2m} \nabla^2\Psi + V\Psi = i\hbar \frac{\partial\Psi}{\partial t}$
$\nabla^2 = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2}$ (Laplacian operator