- #1
trosten
- 47
- 0
Why is it that all the potentials that we use in QM are classical ? For example the columb potential. Shouldnt we use a wave equation for the potential as well as for the position?
Last edited:
Why is it that all the potentials that we use in QM are classical ?
- Thread starter trosten
- Start date
-
- Tags
- Classical Potentials Qm
In summary, all the potentials used in Quantum Mechanics have classical roots and are described by wave equations, except for spin. The second principle of QM states that observables with classical counterparts are quantized, meaning that classical Hamiltonian observables are transformed into self adjoint linear operators. The Coloumb potential, which is a classical E&M potential, serves as the basis for accurately describing atomic properties and dynamics in QM. While more complex phenomena in QED can be described using wave equations, Feynman diagrams are often used instead.
- #2
- 13,348
- 3,104
trosten said:
Because it's natural..??
It's the idea of quantization.Describing interactions at quantum level by means of mathematical objects requiredby the formalism of QM.The second principle of QM (the postulate of quantization) says that for observables with classical correspondent (the spin angular momentum is an example of quantum observable which does not have classical correspondent) we do the quantization by passing all classical Hamiltonian observables viewed as functions from the Poisson algebra of Hamiltonian observables into densly defined self adjoint linear operators acting on th separable Hilbert space of states (defined in the first principle/postulate).So everything has 'classical' roots.The notions of Hamiltonian,Lagrangian,action,field equations,energy,angular momentum,momentum,evolution operators,...Except spin.
Daniel.
- #3
reilly
Science Advisor
- 1,077
- 1
Actually, in virtually any Quantum Field Theory the "potential" does obey a wave eq (like a Klein-Gordan Eq.) And, in classical E&M, potentials must be supplemented by vector potentials as well. The interaction between two charged particles is described by retarded forces/potentials, and thus requires two times. The plain fact is that the math of the retarded interaction is horribly difficult. The classical E&M potential give solvable dynamics for both classical and quantum systems. And the Coloumb Potential gives the basis in QM for a remarkably accurate description of atomic properties and dynamics.
Phenomena like the Lamb shift or the anomalous magnetic moment of the electron can be thought of as coming from a "wave description" of interactions. They involve charges absorbing radiation that the same charge emitted. QED, past lowest order approximations, is exactly a theory with interactions that can be described in terms of wave equations. But we tend not to think along those lines, and more often than not, we tend to think of QED in terms of Feynman diagrams.
Regards,
Reilly Atkinson
Phenomena like the Lamb shift or the anomalous magnetic moment of the electron can be thought of as coming from a "wave description" of interactions. They involve charges absorbing radiation that the same charge emitted. QED, past lowest order approximations, is exactly a theory with interactions that can be described in terms of wave equations. But we tend not to think along those lines, and more often than not, we tend to think of QED in terms of Feynman diagrams.
Regards,
Reilly Atkinson
1. Why do we use classical potentials in quantum mechanics?
One of the main reasons for using classical potentials in quantum mechanics is that they provide a simplified and mathematically tractable way of describing the interactions between particles. These potentials are based on classical physics principles and can be easily applied to quantum systems.
2. Can't we use quantum potentials in quantum mechanics?
While it is possible to use quantum potentials in quantum mechanics, they are often more complex and difficult to work with compared to classical potentials. Additionally, classical potentials are often sufficient for describing the behavior of quantum systems.
3. How accurate are classical potentials in quantum mechanics?
Classical potentials may not always provide a completely accurate description of quantum systems. However, they are often a good approximation and can be used to make predictions that are in agreement with experimental results.
4. Are there any limitations to using classical potentials in quantum mechanics?
One limitation of using classical potentials in quantum mechanics is that they do not account for certain quantum effects, such as tunneling and entanglement. Additionally, they may not accurately predict the behavior of systems at very small scales.
5. Can we use a combination of classical and quantum potentials in quantum mechanics?
Yes, it is possible to use a combination of classical and quantum potentials in quantum mechanics. This approach, known as semi-classical approximation, is often used to describe the behavior of systems that exhibit both classical and quantum behavior.
Similar threads
-
Quantum Physics
-
Quantum Physics
-
Quantum Physics
-
Quantum Physics
-
Quantum Physics
-
Quantum Physics
-
Quantum Physics