# Final Thoughts

In physics, a final state, or final state analysis, is the post-collapse state of a system. In the context of a quantum system, a final state is the state which a quantum system settles into after it has been subject to a perturbation. The final state of a system can be described as the state that is left after the system is "perturbed" from an initial state by an external force. It is the state that the system would be in if it was never disturbed. A final state for a system can be calculated in a number of ways. In the quantum formalism the final state is given by the eigenstates of the initial state, and the eigenstates of the final state. In order to calculate the final state, the Schrödinger equation must be solved. The solutions of the Schrödinger equation are called the eigenstates. The Hamiltonian is then used to calculate the eigenstates of the Hamiltonian. For a quantum system in a ground state, the Schrödinger equation is: where "?" is the reduced Planck constant, formula_2 is the position operator, formula_3 is the momentum operator, and formula_4 is the time-independent Hamiltonian. If the system is in a ground state, then the Hamiltonian is: where the formula_7s are the eigenvalues of the Hamiltonian and formula_8. The state of the system is then given by: where formula_10 is the reduced Planck constant, formula_11 is the eigenstate of the position operator, and formula_12 is the eigenstate of the momentum operator. A quantum system in an excited state can be described by its initial state, along with the additional observable that is the difference between the initial state and the final state. The final state is then the state of the system if it is in an excited state. For a quantum system in an excited state, the Schrödinger equation is: where formula_13 is the initial eigenstate, formula_14 is the final eigenstate, and formula_15 is the time-independent Hamiltonian. If the system is in an excited state then the Hamiltonian is: where the formula_7s are the eigenvalues of the Hamiltonian and formula_8. The state of the system is then given by: where formula_10 is the reduced Planck constant, formula_11 is the eigenstate of the position operator, and formula_12 is the eigenstate of the momentum operator. The final state is the state of the system for all time. In a quantum system, the final state is the state that is left after the system is "perturbed" from an initial state by an external force. It is the state that the system would be in if it was never disturbed. The final state of a system can be described in a number of ways in quantum mechanics. In quantum mechanics, the final state can be described as the state that the system would be in if it was never disturbed. It is the state that the system would be in if it was never perturbed. If the system is in a ground state, then the final state is given by the state of the system at the time the system is in a ground state. The final state is the state that is left after the system is "perturbed" from an initial state by an external force. It is the state that the system would be in if it was never disturbed. If the system is in an excited state, then the final state is also given by the state of the system at the time the system is in an excited state. The final state is the state that is left after the system is "perturbed" from an initial state by an external force. It is the state that the system would be in if it was never disturbed. If the system is in a superposition of two states then the final state is a superposition of both of the states at the time the system is in a superposition. The final state is the state that is left after the system is "perturbed" from an initial state by an external force. It is the state that the system would be in if it was never disturbed. A system in a superposition of states can be described by its initial state, along with the additional observable that is the difference between the initial state and the final state. The final state is then the state of the system if it is in a superposition of states. If the system is in a superposition of states, then the Schrödinger equation is: where formula_13 is the initial eigenstate, formula_14 is