Pretty much the same thing as when ANY type wave activity overlaps.
If a fluid wave from one source meets up with wave in the same fluid, but from a different source, you have overlapping waves. The result can be interference, both destructive and constructive.
The same thing happens when you have EM waves (ie, light) coming from two different sources. This can happen if the EM radiation has a wavelength of one meter (ie, radio waves) or one angstrom (x-rays), or anything in between.
Erwin Schroendinger hypothesized the usefulness (existence?) of a wave function, which can be used to accurately predict the behavior of sub-atomic particles. It has been found that, when predicting such behavior, one can assume that this wave function also acts like a fluid wave or a EM wave. You can accurately predict maxima and minima of the probability of an electron, over time, reaching a specific point in space given two possible paths for that electron. Simply assume that the two possible paths of the electron are like sources of this wave function, then assume the two wave functions overlap (just like other waves), and then do the math -- and, at the end, you have an accurate prediction of the probability that an electron will reach somewhere.
Scientists still debate just what this MEANS -- is this wave function something REAL, or just a mathematical trick that just happens to work? No matter what the case, assuming an overlapping wave function is like other overlapping waves, allows us to predict what will happen.
A wave function is normalized by determining normalization constants such that both the value and first derivatives of each segment of the wave function match at their intersections. If instead you meant renormalization, that is a different problem having to do with elimination of infinities in certain wave functions.
No these are non-overlapping.
A metallic bond is characterized by overlapping atoms.
Math Prelude: Orthogonal wave functions arise as a natural consequence of the mathematical structure of quantum mechanics and the relevant mathematical structure is called a Hilbert Space. Within this infinite dimensional (Hilbert) vector space is a definition of orthogonal that is exactly the same as "perpendicular" and that is the natural generalization of "perpendicular" vectors in ordinary three dimensional space. Within that context, wave functions are orthogonal or perpendicular when the "dot product" is zero. Quantum Answer: With that prelude, we can then say that mathematically, the collection of all quantum states of a quantum system defines a Hilbert Space. Two quantum functions in the space are said to be orthogonal when they are perpendicular and perpendicular means the "dot product" is zero. Physics Answer: The question asked has been answered, but what has not been answered (because it was not was not asked), is why orthogonal wave functions are important. As it turns out, anything that you can observe or measure about the state of a quantum system will be mathematically represented with Hermitian operators. A "pure" state, i.e. one where the same measurement always results in the same answers, is necessarily an eigenstate of a Hermtian operator and any two pure states that give two different results of measurement are necessarily "orthogonal wave functions." Conclusion: Thus, there are infinitely many orthogonal wave functions in the set of all wave functions of a quantum system and that orthogonal property has no physical meaning. When one identifies the subset of quantum states that associated pure quantum states (meaning specifically measured properties) and then two distinguishable measurement outcomes are associated with two different quantum states and those two are orthogonal. But, what was asked was a question of mathematics. Mathematically orthogonal wave functions do not guarantee distinct pure quantum state, but distinct pure quantum states does guarantee mathematically orthogonal wave functions. You can remember that in case someone asks.
For general waves...probably d'Alembert, who solved the one-dimensional wave equation. In quantum it would have to be Schrodinger.
An overlapping wave is called interference. Interference occurs when two or more waves interact with each other, either reinforcing (constructive interference) or canceling out (destructive interference) their amplitudes at certain points.
Sound quality is the term for the bending of overlapping sound wave frequencies through interference.
Symmetric wave functions remain unchanged when particles are exchanged, while antisymmetric wave functions change sign when particles are exchanged.
The phase constant in wave functions represents the starting point of a wave's oscillation. It determines the position of the wave at a specific time and helps in understanding the behavior and properties of the wave.
A shock wave
Sound quality is the term for the bending of overlapping sound wave frequencies through interference.
The term for blending or overlapping sound wave frequencies through interference is called "beats." This phenomenon occurs when two sound waves of slightly different frequencies combine, creating a modulation in volume known as beats.
or studying wave properties
E. I. Peltola has written: 'Comparison of some deuteron wave functions' -- subject(s): Deuterons, Wave functions
A bow wave occurs when an object moves through a medium at a speed greater than the speed of waves in that medium, creating a "V" shape pattern in front of the object. A shock wave, on the other hand, is a sudden change in pressure, temperature, and density in a medium caused by an object moving faster than the speed of sound in that medium, leading to a sharp increase in these properties.
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Wave functions are mathematical functions that describe the behavior of particles in quantum mechanics. Some examples include the wave function for a particle in a box, the harmonic oscillator wave function, and the hydrogen atom wave function. These functions represent the probability distribution of finding a particle in a certain state or position. They are significant in quantum mechanics because they provide a way to predict and understand the behavior of particles at the quantum level.