dded mag as rel

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Robin P. Clark 2026-06-09 09:47:51 +01:00
parent 8f297047bd
commit 390d5b800f
6 changed files with 24 additions and 10 deletions

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![[De_Broglie_Kracklauer.pdf]]
# De-Broglie 1924 QM Thesis
[De_Broglie_Kracklauer.pdf](De_Broglie_Kracklauer.pdf)

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[Ideas](Ideas.md)
[Complex_probabilities](Complex_probabilities.md)
[Complex_probabilities](Complex_probabilities.md)
[Straight Line Motion](Straight%20Line%20Motion.md)
[Magnetism due to special relativity](mag_special_rel.md)

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@ -129,7 +129,7 @@ This is why the **Laplacian appears in the Schrödinger equation**.
## Final intuition
The wavefunction contains two things:
The wave~function contains two things:
**Amplitude**
- how much probability is present

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@ -61,7 +61,7 @@ So the **divide by $2m$** simply comes from the classical kinetic energy formula
## 2. Introduce a wave
Quantum mechanics uses a **wavefunction** $\psi(x,t)$.
Quantum mechanics uses a **wave~function** $\psi(x,t)$.
Take a simple plane wave in 1D:
@ -112,9 +112,9 @@ $$
Substitute this into the second derivative result:
$$
\frac{\partial^2 \psi}{\partial x^2}
=
$$
-\left(\frac{p}{\hbar}\right)^2 \psi
=
$$
-\frac{p^2}{\hbar^2}\psi
$$
Rearrange:
@ -150,6 +150,7 @@ $$
E\psi = \frac{p^2}{2m}\psi + V\psi
$$
Replace $p^2\psi$:
$$
E\psi
=
@ -157,9 +158,7 @@ E\psi
$$
So
$$
E\psi
=
-\frac{\hbar^2}{2m}\frac{\partial^2 \psi}{\partial x^2} + V\psi
E\psi = -\frac{\hbar^2}{2m}\frac{\partial^2 \psi}{\partial x^2} + V\psi
$$
This is where the factor
$$
@ -182,6 +181,7 @@ $$
\frac{\partial \psi}{\partial t} = -i\omega \psi
$$
Multiply by $i\hbar$:
$$
i\hbar \frac{\partial \psi}{\partial t}
=
@ -209,6 +209,7 @@ $$
## 7. Substitute into the equation
We had
$$
E\psi =
-\frac{\hbar^2}{2m}\frac{\partial^2 \psi}{\partial x^2}
@ -216,6 +217,7 @@ E\psi =
$$
Replace $E\psi$:
$$
i\hbar \frac{\partial \psi}{\partial t}
=

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# Standards Notes
[EN298](EN298.md)
[EN60730](EN60730.md)
[EN61508](EN61508.md)

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[Clothing](Clothing.md)
[Cycling](Cycling.md)
[Juggling](Juggling.md)
[Unicycling](Unicycling.md)
[Uni-cycling](Unicycling.md)
[Music](Music.md)