Confusion with superposition of states

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• ntt
In summary, the wavefunction can be written as a linear combination of eigenfunctions due to completeness property. If an electron is excited, when it is relaxing back to ground state, it can be in a superposition of two discrete energy eigenstates. During relaxation, there is a dynamical law that describes the change of coefficient of each eigenstate with time.
ntt
TL;DR Summary
Can an electron be in a superposition of energy eigenstates during relaxation after excited?
Since my major is not physics. My QM knowledge is not pretty good (Mostly self study). I am sorry if this question was asked multiple times in the forum.

I've learned that wavefunction can be written as a linear combination of eigenfunctions due to completeness property.
If an electron is excited. When it is relaxing back to ground state. Can the state of the electron during relaxation a superposition of two discrete energy eigenstates?

If so, during relaxation, is there dynamical law that describes the change of coefficient of each eigenstate with time? (I've looked up the spontaneous emission but still don't have a clear idea what governs the time of relaxation like the design of laser which utilizes a metastable level)

From my understanding, when we observed photon emitted from relaxation, this means we already observe the system which the wave function then has already collapsed to the ground state and the relaxation time is very short. Is my understanding correct?

Any interpretation and correction of my concept and additional reading resources would be greatly appreciated.

Thank everyone in advance for the replies.

You have to carefully distinguish about which eigenstates you talk.

Take a hydrogen atom as a concrete example. You first treat it just as an electron in the Coulomb potential of the nucleus. Then you can evaluate the energy eigenstates of this Hamiltonian. If this were the full story, and your atom is in some energy eigenstate at ##t=0##, then it would stay in this state forever.

Now, however, there's also the electromagnetic field itself, and it's a quantum field, i.e., there are quantum fluctuations, leading to a coupling of the electron to the electromagnetic field. Taking this additional part of the Hamiltonian into account, which can be done perturbatively, you'll get a finite probability for a spontaneous transition from an excited atomic state to a lower atomic state and the emission of a photon.

aaroman
vanhees71 said:
You have to carefully distinguish about which eigenstates you talk.

Take a hydrogen atom as a concrete example. You first treat it just as an electron in the Coulomb potential of the nucleus. Then you can evaluate the energy eigenstates of this Hamiltonian. If this were the full story, and your atom is in some energy eigenstate at ##t=0##, then it would stay in this state forever.

Now, however, there's also the electromagnetic field itself, and it's a quantum field, i.e., there are quantum fluctuations, leading to a coupling of the electron to the electromagnetic field. Taking this additional part of the Hamiltonian into account, which can be done perturbatively, you'll get a finite probability for a spontaneous transition from an excited atomic state to a lower atomic state and the emission of a photon.

Thank you very much for your reply.

Your reply lead my reading to Fermi's Golden rule which is what I was looking for.

vanhees71

1. What is superposition of states?

Superposition of states is a principle in quantum mechanics that states that a quantum system can exist in multiple states at the same time. This means that the system is in a combination of all possible states until it is observed or measured, at which point it will collapse into a single state.

2. How does superposition of states differ from classical physics?

In classical physics, a system can only exist in one state at a time. However, in quantum mechanics, a system can exist in multiple states at the same time, known as superposition. This is one of the key differences between classical and quantum physics.

3. What is the significance of superposition of states in quantum computing?

In quantum computing, the ability to exist in multiple states at the same time allows for the creation of quantum bits, or qubits. These qubits can represent and process much more information than classical bits, making quantum computers potentially much more powerful than classical computers.

4. Can superposition of states be observed in everyday life?

No, superposition of states is a phenomenon that occurs at the quantum level and cannot be observed in everyday life. This is because the act of observing or measuring a system causes it to collapse into a single state, making it impossible to observe superposition in larger, macroscopic objects.

5. How is superposition of states related to the concept of entanglement?

Entanglement is a phenomenon in which two or more particles become connected in such a way that the state of one particle is dependent on the state of the other, even when they are physically separated. Superposition of states is often used to create entangled particles, as the particles must exist in multiple states at the same time in order to become entangled.

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