Is the Energy of a Spin 1/2 Particle Always Equal to h/2?

In summary, a spin 1/2 particle is a fundamental particle with a quantum mechanical property known as spin, which is related to its angular momentum. The energy of a spin 1/2 particle is determined by its mass and spin state, and it plays a significant role in the particle's behavior and stability. The energy of a spin 1/2 particle can be measured through various techniques and can be changed through collisions or exposure to external magnetic fields.
  • #1
Molar
45
19
We know Sz = h/2 [1 0 // 0 -1] for up spin.So can we say that the energy of the electron in this state is h/2 ?
(since Sz |up> = h/2 |up>)Now we consider a Hamiltonian H = [1 0 // 0 -1] which has eigen values +1, -1 and the respective states are
(1 0) and (0 1).
If we see the Schrodinger's equation it gives :
H |1 0 > = 1 * |1 0> which says energy of | 1 0 > is = 1.

We take same hamiltonian, same state, but once we are getting energy eigen value 1/2 ,next time we are getting 1.
Where I am getting it wrong ?
 
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  • #2
Well that's a bit dumb question...Sz includes "1/2" .:H
 

FAQ: Is the Energy of a Spin 1/2 Particle Always Equal to h/2?

What is a spin 1/2 particle?

A spin 1/2 particle is a type of fundamental particle that has a quantum mechanical property known as spin. Spin is a fundamental property of particles and is related to their angular momentum. Particles with spin 1/2 are known as fermions and include particles such as electrons, protons, and neutrons.

What is the energy of a spin 1/2 particle?

The energy of a spin 1/2 particle is determined by its mass and its spin state. The energy of a particle is related to its mass through Einstein's famous equation E=mc². The spin state of a particle can also affect its energy, as particles with different spin states can have different energies.

What is the significance of the energy of a spin 1/2 particle?

The energy of a spin 1/2 particle is significant because it is a fundamental property of the particle that affects its behavior and interactions with other particles. The energy of a particle also plays a role in determining its stability, as particles with higher energies tend to be less stable.

How is the energy of a spin 1/2 particle measured?

The energy of a spin 1/2 particle can be measured through various techniques, such as particle accelerators or spectroscopy. In these experiments, the energy of the particle is determined by analyzing the interactions between particles or by measuring the radiation emitted by the particle.

Can the energy of a spin 1/2 particle be changed?

Yes, the energy of a spin 1/2 particle can be changed through various processes, such as collisions with other particles or by being in an external magnetic field. The change in energy can also result in a change in the spin state of the particle, which can have implications for its behavior and interactions with other particles.

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