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Rick2015
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How many energy eigenstates can "fit" inside a one-dimension box of length L?
Rick2015 said:How many energy eigenstates can "fit" inside a one-dimension box of length L?
Nugatory said:It's not clear what you mean by "fit", but there are an infinite number of energy eigenstates available and any superposition of any number of these is possible. Google for "infinite square well eigenfunction" for more information.
An energy eigenstate is a quantum state in which the energy of the system is well-defined and unchanging. In other words, it is a state of the system that has a definite energy, and this energy does not change over time.
A one-dimensional box is a theoretical model used in quantum mechanics to represent a confined system. The energy eigenstates of a one-dimensional box refer to the possible energy levels that a particle can have within this box, where the particle is confined to one dimension.
The energy eigenstates in a one-dimensional box are important because they represent the allowed energy levels that a particle can have within the box. These states also have corresponding wave functions that can be used to describe the probability of finding the particle at a particular location within the box.
The energy eigenstates inside a one-dimensional box can be calculated using the Schrödinger equation, which is a fundamental equation in quantum mechanics. The solutions to this equation yield the energy eigenstates and corresponding wave functions for a given system.
Yes, the energy eigenstates inside a one-dimensional box have been observed in experiments using quantum systems such as atoms and electrons. These systems can be confined to a one-dimensional box and their energy levels can be measured and compared to the theoretical predictions.