Skip to content

Latest commit

 

History

History
115 lines (98 loc) · 10.9 KB

README.md

File metadata and controls

115 lines (98 loc) · 10.9 KB
Raw

Awesome-Quantum

> A collection of various awesome resources about quantum mechanics, cryptography, computing, and hacking.

5 of the fundamental equations in quantum mechanics:

Schrödinger Equation (time-dependent): $$i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat{H}\Psi(\mathbf{r},t)$$ This equation describes how the quantum state of a system evolves over time. It relates the rate of change of the wavefunction $\Psi$ to the Hamiltonian operator $\hat{H}$, which represents the total energy of the system.

Schrödinger Equation (time-independent): $$\hat{H}\Psi(\mathbf{r}) = E\Psi(\mathbf{r})$$ This is the time-independent form of the Schrödinger equation, used to find the stationary states and energy levels of a system.

Born Rule (probability interpretation): $$\int_{V}|\Psi(\mathbf{r})|^2 dV = 1$$ *This equation states that the square of the wavefunction $|\Psi|^2$ represents the probability density of finding a particle at a given position.

Heisenberg Uncertainty Principle: $$\Delta x \Delta p \geq \frac{\hbar}{2}$$ This principle states that there is a fundamental limit to the precision with which certain pairs of physical properties (such as position and momentum) can be simultaneously measured.

Dirac Equation (relativistic): $$\left(i\hbar\gamma^\mu\partial_\mu - mc\right)\Psi = 0$$ *This is the relativistic wave equation for spin-1/2 particles, proposed by Paul Dirac, which incorporates both quantum mechanics and special relativity. *

Quantum Mechanics:

Quantum Cryptography and Hacking

Books: