How do I introduce Schr\"odinger equation during the quantum mechanics course?

TL;DR

This paper presents a chronological teaching method for introducing the Schrödinger equation in quantum mechanics courses, emphasizing the wave equation and quantum concepts to enhance student understanding.

Contribution

The paper introduces a novel pedagogical approach that starts with the wave equation and derives the Schrödinger equation using fundamental quantum concepts, differing from traditional textbook methods.

Findings

The approach aligns with the original Nuffield A level curriculum.

It differs from most textbook presentations, except Weinberg and Dicke and Wittke.

The method helps clarify the meaning of the quantum wavefunction.

Abstract

In this paper I explain how I usually introduce the Schr\"odinger equation during the quantum mechanics course. My preferred method is the chronological one. Since the Schr\"odinger equation belongs to a special case of wave equations I start the course with introducing the wave equation. The Schr\"odinger equation is derived with the help of the two quantum concepts introduced by Max Planck, Einstein, and de Broglie, i.e., the energy of a photon $E=\hbar\omega$ and the wavelength of the de Broglie wave $\lambda=h/p$. Finally, the difference between the classical wave equation and the quantum Schr\"odinger one is explained in order to help the students to grasp the meaning of quantum wavefunction $\Psi({\bf r},t)$. A comparison of the present method to the approaches given by the authors of quantum mechanics textbooks as well as that of the original Nuffield A level is presented. It is found that the present approach is different from those given by these authors, except by Weinberg or Dicke and Wittke. However, the approach is in line with the original Nuffield A level one.