- #1
anilrapire
- 16
- 0
would someone mind explaining why, in general, degenerate (quantum) states are not orthogonal?
Degenerate quantum states refer to two or more quantum states that have the same energy level. These states are not orthogonal because they cannot be distinguished from each other by any measurement. This means that they have the same probability of being observed, making it impossible to determine their exact state. As a result, they cannot be considered orthogonal, which is a property of states that have distinct and distinguishable properties.
The non-orthogonality of degenerate quantum states has significant implications in quantum mechanics. It means that these states are not independent of each other and cannot be described by a single wave function. This makes it challenging to accurately predict the behavior of these states and can lead to uncertainties in measurements and calculations.
The presence of degenerate quantum states in a quantum system can impact its stability and dynamics. These states can interact and interfere with each other, leading to complex behavior and making it difficult to control the system. Additionally, the non-orthogonality of these states can result in degenerate perturbation, where small changes in the system can cause significant variations in the states' energies.
No, degenerate quantum states cannot be distinguished from each other. This is because, by definition, they have the same energy level and cannot be differentiated by any measurement. However, in some cases, it is possible to break the degeneracy by applying an external perturbation to the system, which can slightly modify the energy levels and allow for their distinction.
Degenerate quantum states are relatively common, especially in simple quantum systems. This is because the number of possible energy levels in a system is limited, and as more particles are added, the likelihood of degeneracy increases. However, in more complex systems, such as atoms with multiple electrons, degenerate states become less prevalent due to the introduction of additional energy levels and interactions between particles.