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Wave function Ψ(r,t) is time dependent. But then why probability [Ψ(r,t)]2 is time independent
Demystifier said:Sometimes it is, when psi(x,t) is an energy eigenstate. (I hope I don't need to explain why.)
The probability wave function, denoted as Ψ(r,t), is a mathematical function used in quantum mechanics to describe the state of a quantum system at a given time. It is a complex-valued function that describes the probability of finding a particle at a certain position in space and time.
The probability wave function is important because it allows us to make predictions about the behavior of quantum systems. By understanding the probability distribution of a particle's position, we can determine the likelihood of its presence in a certain area and make predictions about its future behavior.
When we say that the probability wave function is time independent, it means that it does not change over time. In other words, the probability distribution of the particle's position remains constant throughout time. This is a fundamental property of quantum mechanics and is essential for making accurate predictions about the behavior of quantum systems.
The Schrödinger equation is a mathematical equation that describes the evolution of a quantum system over time. The probability wave function Ψ(r,t) is a solution to the Schrödinger equation, and its time independence is a result of the time-independent nature of the equation itself.
No, the probability wave function Ψ(r,t) cannot be directly observed or measured. It is a theoretical concept that helps us understand the behavior of quantum systems. However, the square of the probability wave function, |Ψ(r,t)|², can be measured experimentally and is related to the probability of finding a particle at a certain position in space and time.