# Quantum mechanics results of a measurement when the system isn’t in an eigenstate

Jul 22, 2022

In quantum mechanics, the act of measurement can cause a sudden change in the state of a system, even when that system wasn’t in an eigenstate to begin with. This effect is called the measurement problem, and it’s one of the key ways in which quantum mechanics differs from classical mechanics.

In classical mechanics, measurements are always assumed to be perfect. That is, when you measure something like the position of a particle, you always get an exact result. There is no such thing as a measurement error.

In quantum mechanics, however, measurements are not perfect. Heisenberg’s uncertainty principle tells us that it’s impossible to measure both the position and momentum of a particle with perfect accuracy. There will always be some uncertainty in the results.

The measurement problem arises when we try to apply this same principle to the act of measurement itself. In classical mechanics, the act of measurement is just another type of interaction between two systems. But in quantum mechanics, the act of measurement can cause a sudden and discontinuous change in the state of a system.

This effect was first noticed by Niels Bohr and Werner Heisenberg in the early days of quantum mechanics. They realized that when you try to measure a quantum system, the act of measurement itself will change the system in a way that is impossible to predict.

This effect is sometimes called the collapse of the wavefunction. What happens is that the wavefunction of the system suddenly changes from a superposition of states to a single eigenstate. The process is completely random and cannot be predicted in advance.

This effect has some strange consequences. For example, it means that we can never know the true state of a quantum system. We can only know the state that we measure.

The measurement problem is still not fully understood, and it continues to be a source of debate and research in quantum mechanics.

## Other related questions:

### Q: What is an eigenstate quantum mechanics?

A: In quantum mechanics, an eigenstate is a state of a system that is an eigenvector of the system’s Hamiltonian.

### Q: How do you know if something is eigenstate?

A: There is no definitive answer to this question, as it depends on the specific situation. However, in general, if a system has a well-defined energy eigenstate, then it is possible to determine whether or not a given state is an eigenstate by solving the SchrÃ¶dinger equation for the system.

### Q: What constitutes a measurement in quantum mechanics?

A: The act of measurement in quantum mechanics is the process of obtaining information about the state of a system. In general, the information obtained in a measurement is probabilistic in nature, meaning that it can be used to predict the likelihood of observing certain outcomes.

### Q: What exactly is an eigenstate?

A: In quantum mechanics, an eigenstate is a state of a system that is an eigenvector of the system’s Hamiltonian. In other words, it is a state of the system that is an eigenvector of the operator that represents the system’s energy.