Superposition principle and continuity

In summary, the conversation discusses the superposition principle and its relation to the continuity of ψ in a potential barrier. The participants question how to prove the continuity of ψ using superposition, and provide an example in a potential barrier. The possibility of getting the answer from the principle of quantum superposition is also mentioned. The conversation concludes that the Schrödinger equation is linear and the superposition principle holds due to its linearity.
  • #1
sciboudy
89
0
hello
i have question : how the superposition principle proves continuity of ψ in potential barrier
 
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  • #2
and how to prove the continuity of psi
 
  • #3
Does this question have any context? Book/paper/whatever?
A discontinuous wave function cannot satisfy the Schroedinger equation (it does not have a spatial derivative), but this has no clear relation to superposition. And it is independent of any explicit potentials.
 
  • #4
okay ... but how to prove continuity of psi by super position ? example in potential barrier
 
  • #5
sciboudy said:
okay ... but how to prove continuity of psi by super position ? example 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.
 
  • #6

1. What is the Superposition Principle?

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.

2. What is an example of the Superposition Principle in action?

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.

3. How does the Superposition Principle relate to continuity?

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.

4. What are the limitations of the Superposition Principle?

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.

5. How is the Superposition Principle used in scientific research?

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.

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