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Quantum Mechanics
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from https://en.wikipedia.org/wiki/Quantum_state
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a quantum mechanical prediction for the system represented by the state. Knowledge of the quantum state and the quantum mechanical rules for the system's evolution in time, exhausts all that can be known about a quantum system.
Quantum states may be defined differently for different kinds of systems or problems. Two broad categories are
wave functions describing quantum systems using position or momentum variables and
the more abstract vector quantum states.
Historical, educational, and application-focused problems typically feature wave functions; modern professional physics uses the abstract vector states. In both categories, quantum states divide into pure versus mixed states, or into coherent states and incoherent states. Categories with special properties include stationary states for time independence and quantum vacuum states in quantum field theory.
from https://physics.stackexchange.com/questions/662433/what-is-a-quantum-state
Generally speaking, a state of a system is some mathematical object that completely describes the system at a particular time...
I think the best way to describe quantum states, is by realizing that they are just a mathematical way of representing real structures or phenomena. The real interpretation of the quantum wave function is still an open question, however, the one thing we do know is, different structures are represented through different states.
Imagine an electron in the hydrogen atom. Forget all the advanced quantum mechanics for a second. Imagine, the electrons are particles revolving in K,L,M,N... shells. From Bohr's theory, you can easily check that electrons in different shells have different energies. The point is, you can have an hydrogen atom in a ground state, where the electron is in K shell. However, you can also have an atom in an excited state M shell, for example. Even though these are both hydrogen atoms, they are different. The quantum wave function or 'state' is a mathematical way of representing these different structures, so that you can easily differentiate between them.
Similarly, there are other examples of this. What I'm getting to, is that a quantum 'state' does not have different properties as such. It is a 'collection' of all the properties of the system you are describing. They are a way of mathematically representing a system, like the different hydrogen atoms in the previous example. It is a mathematical description of a system, that allows you to distinguish or compare it to another system.
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