Exercise 8.15: Spin One-Half Particle | Mike F's Phys 4241

In summary, a spin one-half particle is an elementary particle with a spin quantum number of 1/2, which represents its intrinsic angular momentum. The spin of a particle is measured using a Stern-Gerlach apparatus and is significant in quantum mechanics for understanding the behavior of subatomic particles. Spin one-half particles differ from other spin values as they are fermions and have real-life applications in technologies such as MRI, quantum computing, and spintronics.
  • #1
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Homework Statement


http://mikef.org/files/phys_4241_hw19.pdf
I am having trouble figuring out why the imaginary solutions to the differential equation were thrown out in Exercise 8.15.


Homework Equations





The Attempt at a Solution

 
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  • #2
The didn't throw out any imaginary solutions. The just wrote the solutions in terms linear combinations of real solutions. The coefficients can always be complex.
 

1. What is a spin one-half particle?

A spin one-half particle is a type of elementary particle that has a spin quantum number of 1/2. This means that the particle has a specific intrinsic angular momentum that is quantized in units of 1/2.

2. How is the spin of a particle measured?

The spin of a particle is measured using a device called a Stern-Gerlach apparatus. This device uses a magnetic field to split a beam of particles into two separate beams, with one beam having a spin aligned with the magnetic field and the other beam having a spin opposite to the magnetic field.

3. What is the significance of spin in quantum mechanics?

The concept of spin is crucial in quantum mechanics as it is one of the fundamental properties of particles that cannot be explained by classical physics. It is also important for understanding the behavior of atoms, molecules, and subatomic particles.

4. How does spin one-half differ from other spin values?

Spin one-half particles are fermions, which means they follow the Pauli exclusion principle and cannot occupy the same quantum state. On the other hand, particles with integer spin values, such as spin 0, 1, or 2, are bosons and do not follow this exclusion principle.

5. What are some real-life applications of spin one-half particles?

Spin one-half particles, such as electrons and protons, are commonly used in technologies such as magnetic resonance imaging (MRI), which relies on the spin of protons in the body to create images. They are also used in quantum computing and spintronics, which utilize the spin of electrons to store and process information.

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