# Wave Collapse and Degenerate States - A Quick Question

• BAnders1
In summary, when measuring a quantum particle's observable Q, the eigenvalues can be either degenerate or non-degenerate. If the measurement shows a non-degenerate state, it means that the wave function has collapsed onto that state. When the measurement shows a non-degenerate state, it typically means that the wave function has collapsed to a superposition of all states sharing that eigenvalue. However, the details of the measurement procedure may affect this outcome.
BAnders1
Let's say you have some quantum particle whose eigenvalues for some observable Q are either degenerate or non-degenerate. If you measure the observable and find it to be in a non-degenerate state, then you know that the wave function has collapsed onto this state. Now if you measure the observable and find it to be in a non-degenerate state, does this mean that the particle's wave function has collapsed to a superposition of all states sharing this eigenvalue? My answer before writing this was "I have no idea," but my answer afterwords was "Of course it does." I'd still like to see if my latter answer was wrong, because that would mean something interesting is going on.

It depends on details of the measurement procedure, but typically yes, it collapses to a superposition.

Your latter answer is correct. When a quantum particle is in a non-degenerate state, it means that its wave function has collapsed onto a single eigenstate of the observable in question. However, if the particle is in a degenerate state, it means that its wave function has collapsed onto a superposition of all states sharing that eigenvalue. This is because in a degenerate state, there are multiple possible eigenstates that the particle could be in, and the wave function represents the probability amplitudes for each of these states. So, when measuring the observable, the particle's wave function collapses onto a superposition of all these possible states.

## 1. What is wave collapse and how does it occur?

Wave collapse refers to the phenomenon in quantum mechanics where a particle's wave function collapses into a single definite state when it is observed or measured. This occurs because the act of measurement disturbs the particle's state, causing it to collapse into one of its possible states.

## 2. What are degenerate states in quantum mechanics?

Degenerate states are states of a quantum system that have the same energy level. In other words, they are states that cannot be distinguished from each other based on their energy levels. This often occurs in systems with multiple particles, such as atoms with multiple electrons.

## 3. How do wave collapse and degenerate states relate to each other?

Wave collapse plays a crucial role in understanding degenerate states. When a particle in a degenerate state is observed or measured, its wave function collapses into one of its possible states, breaking the degeneracy and determining its specific energy level. This is why wave collapse is essential in understanding the behavior of degenerate states.

## 4. Can degenerate states exist in classical physics?

No, degenerate states only exist in quantum mechanics. In classical physics, particles can have different energy levels and can be distinguished from each other. However, in the quantum world, particles can exist in degenerate states, which cannot be distinguished based on their energy levels.

## 5. What are some real-life applications of wave collapse and degenerate states?

Wave collapse and degenerate states have many real-life applications, particularly in the fields of quantum computing and quantum cryptography. Understanding and controlling wave collapse is crucial in the development of quantum technologies that rely on superposition and entanglement. Additionally, degenerate states have applications in materials science, such as in the study of superconductivity and magnetism.

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