How Do You Calculate Electron Spin Probabilities from a Wavefunction?

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In summary, the conversation is about finding the probabilities of a measurement finding an electron in a spin state with either spin up or spin down. The equation for the spin state is given and the question is whether the probabilities can be found by squaring the coefficients. The solution is confirmed as correct if the spin state is properly normalized.
  • #1
land
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Simple question regarding spin :)

Homework Statement



An electron is in spin state (superposition of spin eigenstates) given by the wavefunction: [tex]\chi=\frac{1}{3}\chi_+ + \frac{2\sqrt{2}}{3}\chi_-[/tex]. I need to find the probabilities that a measurement would find the electron with spin up or spin down.

Homework Equations



Uh.. you just square the coefficients, right? :)

The Attempt at a Solution



Probably a silly question but this seems too easy. I don't have this as a formula anywhere in my notes or book.. but to find the probability of spin up, you just square (1/3), and to find the probability of spin down, it's just the square of 2sqrt(2)/3... right?
 
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  • #2
land said:

Homework Statement



An electron is in spin state (superposition of spin eigenstates) given by the wavefunction: [tex]\chi=\frac{1}{3}\chi_+ + \frac{2\sqrt{2}}{3}\chi_-[/tex]. I need to find the probabilities that a measurement would find the electron with spin up or spin down.

Homework Equations



Uh.. you just square the coefficients, right? :)

The Attempt at a Solution



Probably a silly question but this seems too easy. I don't have this as a formula anywhere in my notes or book.. but to find the probability of spin up, you just square (1/3), and to find the probability of spin down, it's just the square of 2sqrt(2)/3... right?

If it's properly normalized, that will do it.
 
  • #3
OlderDan said:
If it's properly normalized, that will do it.

Thanks! :)
 

FAQ: How Do You Calculate Electron Spin Probabilities from a Wavefunction?

1. What is spin in science?

Spin in science refers to the intrinsic angular momentum of a particle. It is a quantum property that can be either positive or negative, and it is an important characteristic in the study of subatomic particles.

2. How is spin measured?

Spin is measured in units of angular momentum, typically represented by the variable "s". The maximum spin a particle can have is determined by its mass and charge, and is denoted as 2s+1. For example, an electron has a spin of 1/2, while a proton has a spin of 1.

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

Spin plays a crucial role in quantum mechanics as it affects the behavior and properties of particles. It is used to classify particles into different categories, and it also has implications in the formation of atomic and molecular structures.

4. Can the spin of a particle change?

No, the spin of a particle is considered an intrinsic property and cannot be changed. However, the direction of spin can be altered, which is known as spin flipping. This can happen through interactions with other particles or through the application of magnetic fields.

5. How does spin impact our daily lives?

Although spin is a fundamental concept in physics, it also has practical applications in our daily lives. For example, the spin of electrons is used in technologies such as MRI machines and computer hard drives. It also plays a role in determining the chemical properties of elements and compounds.

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