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How do you show that a wave function is a solution to the time- independent Schrodinger equation for a simple harmonic oscillator?
Wiki User
∙ 12y ago
You should substitute your solution in the equation. If the solution is correct you will receive equality. Otherwise your solution is wrong.
Wiki User
∙ 12y ago
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What evidence did Erwin Schrodinger have to support is theory?
When Schrodinger applied his mathematical formulae to the permitted states of an electron in a hydrogen atom, he found they perfectly matched the Bohr Model, which had perfectly predicted hydrogen spectral lines. For Schrondinger, that was good enough for him to publish his work. Max Born later showed that the Schrodinger Equation could be used to accurately predict particle scattering from a nucleus. However, Born showed that this would only work if one assumes that the cross-product of Schrodinger's Wave Function represents the probability of a point charge being in a specific place; something that Schrodinger never accepted.
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.
If the electron in a hydrogen atom obeyed classical mechanics instead of quantum mechanics would it emit a continuous spectrum or a line spectrum?
In some text books on physical chemistry it is stated that if an electron followed the classical laws of mechanics it would continue to emit energy in the form of electromagnetic radiation until it fell to the nucleus. It is not sensible to consider the spectrum of emitted electromagnetic radiation because its wavelength is a function of the Schrodinger equation under the influence of the Hamilton operator. So my only have desecrate values. A classical picture of the atom would not obey the Schrodinger equation so there is no way of predicting the way it would emit energy.
How did Schrodinger and De Broglie change Bohr's model of an atom?
Neils Bohr made the ASSUMPTION that electrons could only exist in discrete energy levels when the electrostatic field of a nucleus -- he made no attempt to show WHY this was so. Louis de Broglie postulated that electron movement could be described as a wave, with the wavelength being equal to Planck's Constant divided by the electron's momentum. Starting with this postulate, one can derive that the only permitted radial orbits of an electron are those with a circumference equal to a multiple of these wavelengths. Erwin Schrodinger devised a mathematical formula for which one could derive these energy levels -- and a lot more. As such, Schrodinger's Equation was more fundamental to our understanding of sub-atomic reality. Schrondinger viewed his wave function (more precisely, the product of the wave function) as the charge density of a smeared-out electron. Although you didn't ask, it was Max Born who showed that the wave-function product was, instead, the probability of finding a point-like electron at a specific place and time.
What is Einstein's photoelectric equation?
E(photon energy)=K.E+Work Function
Derivation of magnetic quantum number from schrodinger wave equation?
equation is a double differential relate to the energy of particle with wave function
How do you convert DC to AC in an oscillator?
that is the function of the oscillator
What is the physical interpretation of bessel function?
spherical bessel function arise in the solution of spherical schrodinger wave equation. in solving the problem of quantum mechanics involving spherical symmetry, like spherical potential well, the solution that is the wave function is spherical bessel function
What evidence did Erwin Schrodinger have to support is theory?
When Schrodinger applied his mathematical formulae to the permitted states of an electron in a hydrogen atom, he found they perfectly matched the Bohr Model, which had perfectly predicted hydrogen spectral lines. For Schrondinger, that was good enough for him to publish his work. Max Born later showed that the Schrodinger Equation could be used to accurately predict particle scattering from a nucleus. However, Born showed that this would only work if one assumes that the cross-product of Schrodinger's Wave Function represents the probability of a point charge being in a specific place; something that Schrodinger never accepted.
What are the independent variables of a function?
An independent variable of a function is the variable that you cannot change by changing the other. Changes to it are not caused by the equation. If you want to graph how the money you invest in a bank account against the time that the money has been in the account, time is the independent variable. This is because the time will change at a constant rate, no matter how much or how often the money collects interest. If you change the equation, the money earned will change, but the time will not.
In the equation V equals πr 3 the volume of a sphere V is a function of R the spheres radius. What is the independent quantity in this function?
The volume of a sphere = 4/3*pi*radius3
Is this equation a function y equals 3squared plus 2x minus 3 is this a function?
You can tell if an equation is a function if for any x value that you put into the function, you get only one y value. The equation you asked about is the equation of a line. It is a function.
What is an inhomogeneous differential equation?
It is one which has a function that does not contain the dependent variable. For example, (dy/dx) + y = f(x) is inhomogeneous but (dy/dx) + y = 0 is not. ( f(x) is a function of the independent variable)
The domain of a function is repersentative of which one of the following characteristics of the function?
The domain of the function means, for what values of the independent variable (input value) (or variables) is the function defined. If you have an equation of the type:y = f(x) ("y" somehow depends on "x") then the domain is all the values that "x" can take.
What is the basic purpose and function of an independent laboratory?
basic purpose and function of an independent laboratory
What type of oscillator has got frequency stability?
A: desirable oscillator will have no frequency deviation as a function of external influences such as temperature and more. Stability is measured as a % factor considering outside interferences
An equation that describes a function?
a function rule
