Spin, linear momentum and orbital angular momentum

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SUMMARY

The discussion centers on the relationship between electron spin, linear momentum, and orbital angular momentum. It is established that when electron spin is perpendicular to linear momentum, the orbital angular momentum cannot be zero. Conversely, when the spin and linear momentum are parallel, the orbital angular momentum is indeed zero. The conversation clarifies that the focus is on the component of angular momentum L_z rather than the total angular momentum L^2.

PREREQUISITES
  • Understanding of quantum mechanics concepts, specifically electron spin.
  • Familiarity with linear momentum and its implications in quantum physics.
  • Knowledge of orbital angular momentum and its components, particularly L_z and L^2.
  • Basic grasp of vector relationships in quantum states.
NEXT STEPS
  • Study the mathematical representation of electron spin and its implications in quantum mechanics.
  • Research the properties of orbital angular momentum and its components in quantum systems.
  • Explore the relationship between linear momentum and angular momentum in quantum mechanics.
  • Learn about the significance of L_z in quantum mechanics and its applications.
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics, as well as researchers exploring the properties of angular momentum in quantum systems.

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How to prove when electron spin is perpendicular to linear momentum, orbital angular momentum can't be 0.
And when they are paralleled, orbital angular momentum is 0.
Thanks.
 
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Your statements are not true. Orbital angular momentum does not depend on spin direction.
 
ad6190 said:
How to prove when electron spin is perpendicular to linear momentum, orbital angular momentum can't be 0.
And when they are paralleled, orbital angular momentum is 0.
Thanks.
I think you are talking abput L_z, and not L^2.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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