Getting Started with Notebook

Welcome to Notebook.

Heading Example

This is a paragraph with some bold and italic text.

Complex Math Verification

Testing the rendering of advanced formulas:

The Quadratic Formula

Given a quadratic equation of the form ax2+bx+c=0ax^2 + bx + c = 0, the solutions for xx are given by:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Heisenberg's Uncertainty Principle

In quantum mechanics, the uncertainty principle states that the more precisely the position of some particle is determined, the less precisely its momentum can be predicted:

ΔxΔp≥ℏ2\Delta x \Delta p \geq \frac{\hbar}{2}

In the equation above, ℏ\hbar is the reduced Planck constant (where ℏ=h2π\hbar = \frac{h}{2\pi}).

Additional Physics Examples

Schrödinger's Equation (Time-independent)

The fundamental equation of non-relativistic quantum mechanics:

H^ψ=Eψ\hat{H}\psi = E\psi

Maxwell's Equations (Differential form)

The foundations of classical electromagnetism:

∇⋅E=ρϵ0\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} ∇⋅B=0\nabla \cdot \mathbf{B} = 0 ∇×E=−∂B∂t\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} ∇×B=μ0(J+ϵ0∂E∂t)\nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \epsilon_0\frac{\partial \mathbf{E}}{\partial t}\right)