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It depends on the hamiltonian but it would be of the form of a regular plane wave.
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This describes the wavelike behaviour of either one electron or a pair of electrons in an atom.?
You think probable to a wave function.
How is the electron cloud related to the modern model of an atom?
The atom where we are most likely to find an electron. this area is called the electron cloud.
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
What is well behaved wave function?
List of the characteristics a well-behaved wave function are ..The function must be single-valued; i.e. at any point in space, the function must have only one numerical value.The function must be finite and continuous at all points in space. The first and second derivatives of the function must be finite and continuous.The function must have a finite integral over all space.
Who produced mathematical equations to describe the wave-like behavior of electron?
Erwin Schrödinger. However, the wave-like behavior of his famous equation is actually a probability function that can be applied to any quantum state, not just position and not just for an electron.
What is the motion of an electron inside a spherical region of uniform unit charge if its kinetic energy is simple harmonic motion about the center of the sphere?
The motion of an electron inside a spherical region of uniform unit charge if its kinetic energy is simple harmonic motion about the center of the sphere is a wave. That is, its motion can be expressed as that of a wave. On the surface, this appears to be a question about the wave-nature of the electron. It was discovered by a cat named DeBroglie that the motion of an electron (and other things) could be described by a mathematical "gimmick" called a wave function. We now call this the de Broglie hypothesis. Recall that when we wander about the quantum mechanical universe, we find that there are a number of instances where something in that area of ever-so-small things acts both like a particle and like a wave. It will, depending on the way we observe the behavior of this "thing" we're looking at, act like one or the other. This leads to the idea of wave-particle duality. And it was Louis de Broglie who ideated this stuff. Light is electromagnetic energy, but light acts like a particle in some instances. An electron is a particle, the fundamental carrier of the negative electrostatic charge. But its behavior can be expressed in terms of a wave function (de Broglie's wave mechanics). It was de Broglie who joined light to the "regular matter" of the quantum mechanical universe with this idea, which he put forth in his PhD thesis. He bagged a Nobel Prize for this work, and he deserved it. Bottom line here is that the electron can be viewed through the lens of a wave equation (a wave function) when it is sailing around in the quantum mechanical world. Links can be found below to relevant posts.
This describes the wavelike behaviour of either one electron or a pair of electrons in an atom.?
You think probable to a wave function.
How is the electron cloud related to the modern model of an atom?
The atom where we are most likely to find an electron. this area is called the electron cloud.
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
what is wave function?
The official definition for the word wave function is "a function that satisfies a wave equation and describes the properties of a wave."
Is sound wave electron?
no.
What is well behaved wave function?
List of the characteristics a well-behaved wave function are ..The function must be single-valued; i.e. at any point in space, the function must have only one numerical value.The function must be finite and continuous at all points in space. The first and second derivatives of the function must be finite and continuous.The function must have a finite integral over all space.
Who produced mathematical equations to describe the wave-like behavior of electron?
Erwin Schrödinger. However, the wave-like behavior of his famous equation is actually a probability function that can be applied to any quantum state, not just position and not just for an electron.
How will you calculate potential if the wave function is given?
Square the wave function.
Is an electron a standing wave?
No -- an electron is a point particle with mass, charge, and spin. The probability that you will find an electron at a specific point can, however, often be calculated by wave functions. Any moving mass can be considered either a particle or a wave. Its properties can be defined via the deBorlie wave equation.
Shapes of electron orbital are determined by what equations?
Schrodinger wave equation
What is meant by overlapping wave functions?
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.
