Tag: Harmonic

Analyze the Harmonic Oscillator with SymPy

SymPy is a powerful Python library for symbolic mathematics. In this blog we will use its functions to explore the dynamics of the damped harmonic oscillator and demonstrate the power of the library in classical mechanics. Here are the most important functions that we will use in this post [1]: S...

Solving the Schrödinger Equation for Quantum Harmonic Oscillators.

The Schrödinger equation can be thought of as the equivalent to the Newton’s second law but in the quantum world. In the Schrödinger equation, the wave function (Ψ) is used to describe the quantum particle. The quantum Hamiltonian (H) is an operator which corr...

Solution to the Simple Harmonic Motion Differential Equation

Simple harmonic motion (SHM) is a relatively common aspect of classical mechanics and in this article I will be solving the following differential equation that illustrates SHM: Note that this does indeed represent SHM if we recall the definition that SHM occurs when an object is subject to a...

Solution to the Simple Harmonic Motion Differential Equation

Simple harmonic motion (SHM) is a relatively common aspect of classical mechanics and in this article I will be solving the following differential equation that illustrates SHM: Note that this does indeed represent SHM if we recall the definition that SHM occurs when an object is subject to a...