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There are two parts to this. First is, "What is the physical significance of a wave function?" Secondly, "Why do we normalize it?"
To address the first:
In the Wave Formulation of quantum mechanics the wave function describes the state of a system by way of probabilities. Within a wave function all 'knowable' (observable) information is contained, (e.g. position (x), momentum (p), energy (E), ...). Connected to each observable there is a corresponding operator [for momentum: p=-i(hbar)(d/dx)]. When the operator operates onto the wave function it extracts the desired information from it. This information is called the eigenvalue of the observable... This can get lengthy so I'll just leave it there. For more information I suggest reading David Griffith's "Introduction to Quantum Mechanics". A math knowledge of Calculus II should suffice.
To address the second:
Normalization is simply a tool such that since the probability of finding a particle in the range of +/- (infinity) is 100% then by normalizing the wave function we get rid of the terms that muddy up the answer the probability.
An un-normalized wave function is perfectly fine. It has only been adopted by convention to normalize a wave function.
ex. un-normalized wave function (psi is defined as my wave function)
- The integral from minus infinity to positive infinity of |psi|^2 dx = 2pi
ex. normalized wavefunction
- The integral from minus infinity to positive infinity of |psi|^2 dx = 1
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Why wave function complex?
because position of a particle in a wave (performing oscillations) is dependent on both time and the energy it is recieving.....
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The requirement on a wave function is not that it has to be finite but that it has to be finite when integrated over all of space, although the first usually follows from the second (there are exceptions). This is because integrating a wave function over a region of space gives a measure of finding the particle (or whatever the wave function describes) in that region of space. Now, one would reasonably expect that if one would integrate over all of space one would find a finite answer. This is because the chance to find the particle somewhere should be 100%. If the integral is infinite this means the chances of finding the particle are also infinite, which is not a sensible concept in chance theory.
Why wave function complex?
because position of a particle in a wave (performing oscillations) is dependent on both time and the energy it is recieving.....
Why should wave function be single valued and finite?
Type your answer here... the wave function associated with the particle , and it is must be single valued of position and time , when two values are found that means the particle exists in two different places , which is impossible yet
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Light is both a wave and a particle depending on circumstances; this is referred to as the wave-particle duality of light.
Why light posses dual nature?
light travel as a wave but it carries photon which is consider to be a particle.so photon done function as a particle and wave motion made effect as wave.
Is sound a particle or wave?
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What is the role of an observer in wave function collapse?
The question itself is controversial, as we're not sure if the observer has anything to do with the wave collapse. However, once the ability to observe (or interact) with a given particle is enabled, the wave-function or probability wave of that particle peaks, or collapses into a finite quantity. As said, we're not sure if a conscious observer has anything to do with it, or if it has to do with physical interactions in and of themselves. Another opinion: The observer has nothing to do with the collapse of the wave function. It is the measurement acting on the the wave function that does the collapsing. The part about which we are uncertain (we, as in physicists) is whether nature performs the measurement before we do and we get the result, or if nature leaves the wave function as a superposition until we measure it. This is the fundamental question of Schrodinger's cat in a box paradox.
Why does a wave function has to be finite?
The requirement on a wave function is not that it has to be finite but that it has to be finite when integrated over all of space, although the first usually follows from the second (there are exceptions). This is because integrating a wave function over a region of space gives a measure of finding the particle (or whatever the wave function describes) in that region of space. Now, one would reasonably expect that if one would integrate over all of space one would find a finite answer. This is because the chance to find the particle somewhere should be 100%. If the integral is infinite this means the chances of finding the particle are also infinite, which is not a sensible concept in chance theory.
What is particle wave?
a partical wave is the name of normal wave
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Is the emission of electromagnetic radiation by an excited atom is it a wave or a particle?
a particle traveling in wave form.
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