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The wavefunction describes the state of a system. When an operator 'acts on' the wavefunction are we saying, in layman's terms, that the operator is changing the state of the system?
kuruman said:Yes, unless the the wavefunction is a "proper" state (eigenstate) of the operator in which case the state of the system after the application of the operator is the same as before. In other words, if the state of the system is a mixture of more than one proper states, when the operator acts on the system, the wavefunction of the system is changed to one of these proper states. Any subsequent "action" of the operator on the ensuing proper state leaves it unchanged.
When we say that operators 'act on' the wavefunction, we mean that they manipulate or transform the wavefunction in some way. Operators are mathematical tools used in quantum mechanics to describe the behavior of physical systems.
Operators are used in quantum mechanics to describe the physical properties of a quantum system, such as position, momentum, energy, and spin. They allow us to make predictions about the behavior of particles in a quantum system.
Operators can affect the wavefunction in different ways, depending on the specific operator being used. Some operators, such as the position operator, shift the wavefunction to a different position in space. Others, like the momentum operator, change the shape and direction of the wavefunction.
When multiple operators act on the wavefunction, they are applied in succession and their effects are combined. This allows us to describe more complex physical systems and make more detailed predictions about their behavior.
Yes, there are specific mathematical rules and equations that govern how operators act on the wavefunction. These rules, known as the rules of quantum mechanics, dictate how operators are applied to the wavefunction and how the resulting wavefunction is interpreted.