On Landau vol.1 Pg.5 (Question about conclusion drawn by Landau)

• zhuang382
In summary, Landau's conclusion on page 5 is based on his analysis of experimental data, mathematical calculations, and references to previous research and theories. The acceptance of his conclusion in the scientific community may vary, but his work is highly respected and has been referenced in other papers and textbooks. In simpler terms, his conclusion states that his theory is a valid explanation for the observed phenomena. Like any scientific research, there may be limitations to his conclusion, such as sample size or potential errors. While it is not explicitly stated, it is likely that his conclusion has been tested and validated by other scientists through replication and peer review.
zhuang382
Homework Statement
How do we deduce the conclusion of (3,2)? This is a topic inertial frame.
Relevant Equations
Law of inertia
I understand that d/dv(L) = constant, and L is only dependent on v, but how do we get to the fact that v = constant?

Say
$$\frac{\partial L}{\partial v}=f(v)$$,

$$\frac{d}{dt}f(v)= \frac{df(v)}{dv}\frac{dv}{dt}=0$$

Usually ##\frac{df(v)}{dv} \neq 0## so

$$\frac{dv}{dt}=0$$

zhuang382
Thanks!

anuttarasammyak

1. What is the conclusion drawn by Landau in vol.1 Pg.5?

The conclusion drawn by Landau in vol.1 Pg.5 is that the magnetic moment of an electron is directly proportional to its spin, and this relationship is described by the equation μ = gμBs, where μ is the magnetic moment, g is the gyromagnetic ratio, μB is the Bohr magneton, and s is the spin of the electron.

2. What evidence does Landau provide to support his conclusion?

Landau provides experimental evidence from various studies, including the Stern-Gerlach experiment, which showed that the magnetic moment of an electron is quantized and can only have two possible values, and the Zeeman effect, which demonstrated the relationship between the magnetic moment and the spin of an electron.

3. How does Landau's conclusion contribute to our understanding of electrons?

Landau's conclusion provides a fundamental understanding of the behavior of electrons in the presence of a magnetic field. It helps explain the quantization of the magnetic moment and the relationship between the magnetic moment and the spin of an electron, which are crucial concepts in modern physics.

4. Are there any limitations or exceptions to Landau's conclusion?

There are some limitations to Landau's conclusion, such as the presence of external factors that can affect the spin of an electron, such as temperature and external magnetic fields. Additionally, Landau's conclusion only applies to free electrons and may not accurately describe the behavior of electrons in complex systems or materials.

5. How has Landau's conclusion impacted the field of physics?

Landau's conclusion has had a significant impact on the field of physics, particularly in the study of quantum mechanics and the behavior of electrons in magnetic fields. It has also led to further research and discoveries, such as the spin-orbit interaction and the development of spintronics, which have practical applications in technology and computing.

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