Differential Equations in Quantum Mechanics and Schrödinger Equation

Year : 2025 | Volume : 01 | Issue : 01 | Page : 15 25
    By

    Pooja Jain,

  1. Research Scholar, Independent Researcher, Indor, India

Abstract

In this study we investigate how differential equations play a role in quantum mechanics, focusing mainly on the role of a prominent one, Schrödinger’s equation, which governs the behavior of quantum systems. In time two the mathematical picture of the wave nature of particles at quantum scales is provided, and the resulting equations are Schrödinger’s equation, both in its time dependent as well as in its time independent form. The time dependent Schrödinger equation is used to describe how a quantum state evolves over time, whereas the time independent version is used to analyze systems that have fixed energy levels like particles in a potential well. Crossing solutions to Schrödinger’s equation produce these wave functions, a treasure trove of information as to how a particle will behave, and even allow us to calculate measurable such as energy and angular momentum. In addition, the study discusses how to apply boundary conditions and potential functions to solve Schrödinger’s equation to specific quantum systems such as the harmonic oscillator and hydrogen atom. When we solve these differential equations, we get deeper insight into fundamental quantum phenomena, which is useful for future progress in quantum computing, nanotechnology, and atomic physics.

Keywords: Quantum mechanics, schrödinger’s equation, differential equations, time-independent

[This article belongs to Emerging Trends in Symmetry ]

How to cite this article:
Pooja Jain. Differential Equations in Quantum Mechanics and Schrödinger Equation. Emerging Trends in Symmetry. 2025; 01(01):15-25.
How to cite this URL:
Pooja Jain. Differential Equations in Quantum Mechanics and Schrödinger Equation. Emerging Trends in Symmetry. 2025; 01(01):15-25. Available from: https://journals.stmjournals.com/etsy/article=2025/view=208052


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Regular Issue Subscription Review Article
Volume 01
Issue 01
Received 11/11/2024
Accepted 12/12/2024
Published 16/04/2025
Publication Time 156 Days
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