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How do I introduce Schr\"odinger equation during the quantum mechanics course?
Physics Education · Submitted 29 Oct 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim However, the approach is in line with the original Nuffield A level one.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper I explain how I usually introduce the Schr\"odinger equation during the quantum mechanics course. | contribution 0.96 | 0.86 | 0.05 | asserted 0.93 |
| s1 | My preferred method is the chronological one. | method 0.72 | 0.80 | 0.08 | asserted 1.00 |
| s2 | Since the Schr\"odinger equation belongs to a special case of wave equations I start the course with introducing the wave equation. | method 0.99 | 0.84 | 0.05 | asserted 0.99 |
| s3 | 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 $\lambda=h/p$. | method 0.99 | 0.68 | 0.05 | asserted 1.00 |
| s4 | 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 $\Psi({\bf r},t)$. | method 0.89 | 0.83 | 0.09 | asserted 0.98 |
| s5 | 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. | contribution 0.62 | 0.79 | 0.06 | asserted 0.96 |
| s6 | It is found that the present approach is different from those given by these authors, except by Weinberg or Dicke and Wittke. | result 1.00 | 0.90 | 0.32 | asserted 1.00 |
| s7 | However, the approach is in line with the original Nuffield A level one. | result 0.98 | 0.66 | 0.23 | asserted 0.98 |
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Original 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.
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