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sciboudy
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hello
i have question : how the superposition principle proves continuity of ψ in potential barrier
i have question : how the superposition principle proves continuity of ψ in potential barrier
I don't understand the "by superposition" requirement. Since ψ satisfies the Schrödinger equation, it's differentiable, and every differentiable function is continuous.sciboudy said:okay ... but how to prove continuity of psi by super position ? example in potential barrier
The Superposition Principle is a fundamental concept in physics that states that when two or more waves or other linear systems are present in the same space, the resulting wave or system is the sum of the individual waves or systems. In simpler terms, it means that the combined effect of multiple waves is equal to the sum of their individual effects.
A common example of the Superposition Principle is when two or more sound waves, such as from different musical instruments, overlap in the same space. The resulting sound that is heard is a combination of the individual sounds from each instrument, demonstrating the principle of superposition.
The Superposition Principle is closely related to the concept of continuity. Continuity refers to the smoothness and uninterrupted flow of a function or system. The Superposition Principle states that if a system is continuous, then the resulting wave or system from the combination of multiple waves will also be continuous.
The Superposition Principle is only applicable to linear systems, meaning that the resulting wave or system is directly proportional to the individual waves. It also assumes that there are no interactions or interference between the individual waves. In reality, these assumptions may not always hold true, limiting the applicability of the Superposition Principle.
The Superposition Principle is a valuable tool in scientific research, particularly in fields such as physics and engineering. It allows scientists to understand and analyze complex systems by breaking them down into simpler components and studying their individual effects before combining them. This principle is also used in various technologies, such as in signal processing and telecommunications, to manipulate and transmit signals.