ivylove Posted June 27, 2017 Posted June 27, 2017 How can an electron position probability that represents a positive value or zero represent wave interference?
Eise Posted June 29, 2017 Posted June 29, 2017 How can an electron position probability that represents a positive value or zero represent wave interference? It can't. But the wave function can. Just calculate the wave function, multiply it with its complex conjugate, and voila, you have your probability distribution. 1
ivylove Posted June 30, 2017 Author Posted June 30, 2017 (edited) How can a probability distribution that originates from an electron position probability represent a negative value? What about the gauge? Edited June 30, 2017 by ivylove
swansont Posted July 1, 2017 Posted July 1, 2017 How can a probability distribution that originates from an electron position probability represent a negative value? What about the gauge? Represent a negative value of what?
Eise Posted July 1, 2017 Posted July 1, 2017 (edited) How can a probability distribution that originates from an electron position probability represent a negative value? What about the gauge? I suggest you read this. This picture more or less says it all: First picture is the wave function for several energies, second its square, i.e. the probability distribution, third the energy levels. As you see the probability distribution is always >= 0, and total chance for every of the three distributions is 1. Clear? PS See also here. Edited July 1, 2017 by Eise 2
ivylove Posted July 3, 2017 Author Posted July 3, 2017 Is the original wave function a solution to Schrodinger's wave equation?
studiot Posted July 3, 2017 Posted July 3, 2017 Is the original wave function a solution to Schrodinger's wave equation? Yes and no. Schrodingers wave equation is a differential equation of motion and applied pretty generally. As such it has many solutions, most of which are useless to us. We need to select the apppropriate one by applying the appropriate boundary conditions. This is where the pictures Eise showed you come in.. They are for what is called a 'particle in a box' or a potential well which means that a negatively charged particle (electron) is subject to a potential well near the positively charged nucleus due to electrostatic interaction. The solution must have 'nodes' at the box edges (points of zero amplitude) like a standing wave on a string in classical mechanics. It is this requirement that introduces the quantisation into the mathematics of the origianl equation.
ivylove Posted July 5, 2017 Author Posted July 5, 2017 (edited) The negative value of the original wave function does not satisfy the parameters of Schrodinger's wave equation that represents the position probability of an electron which is depicted with a positive value of a probability or zero; consequently, the wave function is not a valid solution to Schrodinger's wave equation. Do you agree? Edited July 6, 2017 by ivylove
swansont Posted July 6, 2017 Posted July 6, 2017 The negative value of the original wave function does not satisfy the parameters of Schrodinger's wave equation that represents the position probability of an electron which is depicted with a positive value of a probability or zero; consequently, the wave function is not a valid solution to Schrodinger's wave equation. Do you agree? The probability is the square of the wave function, not the wave function.
ivylove Posted July 6, 2017 Author Posted July 6, 2017 Is Schrodinger's wave equation representing an electron position probability?
studiot Posted July 6, 2017 Posted July 6, 2017 Is Schrodinger's wave equation representing an electron position probability? No I told you that in post#7. Try asking questions directly related to what others have told you and you will get much more out of the conversation.
ivylove Posted July 6, 2017 Author Posted July 6, 2017 (edited) If Schrodinger's wave equation does not represent a probability then what wave structure does it represent (gauge)? Edited July 7, 2017 by ivylove
swansont Posted July 7, 2017 Posted July 7, 2017 If Schrodinger's wave equation does not represent a probability then what wave structure does it represent (gauge)? The wave function is a probability function. When you square it you get the probability. The wave equation (along with boundary conditions) dictates how the wave function must behave.
ivylove Posted July 7, 2017 Author Posted July 7, 2017 (edited) Got it. The end. Edited July 7, 2017 by ivylove
studiot Posted July 7, 2017 Posted July 7, 2017 What structure is Schrodinger's wave equation representing? I am not questioning the validity of the wave function. I am questioning the validity of Schrodinger's wave equation. Only one of your posts is more than one line long. Why would anyone put more effort into answering than this? Are you having trouble with the English language? What level should we be pitching answers at mathematical or just explanatory?
ivylove Posted July 7, 2017 Author Posted July 7, 2017 (edited) What structure is Schrodinger's wave equation representing? I'm interested in the validity of Schrodinger's wave equation that the wave function originates. It's either a probability or gauge. I cannot develop the argument unless I know the structure that Schrodinger's wave equation is representing. Edited July 7, 2017 by ivylove
studiot Posted July 7, 2017 Posted July 7, 2017 (edited) What structure is Schrodinger's wave equation representing? I'm interested in the validity of Schrodinger's wave equation that the wave function originates. It's either a probability or gauge. I cannot develop the argument unless I know the structure that Schrodinger's wave equation is representing. Well I have been thinking about a suitable description for you. This would entail quite a bit of work for me. BUT With that response to my last post I don't believe you would actually read it, any more than you appear to have read Eise's good efforts on your behalf. I see he hasn't bothered again. If I posted some mathematics would you be able to understand it? In theory you are the one challenging established mathematical physics so you should be the one posting supporting mathematics. We can only help you if we all work together. Edited July 7, 2017 by studiot
ivylove Posted July 7, 2017 Author Posted July 7, 2017 (edited) In Schrodinger's paper "An Undulatory theory of the mechanics of Atoms and Molecules" (1926), Schrodinger states the wave function is based on Maxwell's electromagnetic theory. "The wave-function physical means and determines a continuous distribution of electricity in space, the fluctuations of which determine the radiation by laws of ordinary electrodynamics." (Schrodinger, Abstract). Maxwell's electromagnetic field originates from Faraday's induction effect that represents a massless electromagnetic induction field that cannot be used to represent the structure of an atom or molecule that has a mass which proves Schrodinger's wave equation and quantum mechanics based on Maxwell theory are physically invalid. Schrodinger, Erwin. An Undulatory theory of the Mechanics of Atoms and Molecules. Physical Review. 28 (6):1049-1070. 1926. Edited July 7, 2017 by ivylove
ivylove Posted July 11, 2017 Author Posted July 11, 2017 (edited) The conjugate complex is also based on Maxwell's theory. "Denoting the conjugate complex value by a bar, this is YY*..........(28)". (Schrodinger, p. 1065). "The fluctuation of the charge will be governed by the Eq. 28, applied to the special case of the hydrogen atom. To find the radiation, that by electrodynamics will originate from these fluctuating charges, we have simply to calculate the rectangular components of the total electric moment by multiplying (28) by x, y, z respectively, then integrating over space, e.g." (Schrodinger, p. 1066). Schrodinger is using the electric field radiated by an electron to represent the structure of a hydrogen atom which is physically invalid since Maxwell's massless electromagnetic field cannot be used to represent the structure of a H atom that has a mass. Also, Maxwell's expanding electromagnetic field cannot maintain the particle structure of a hydrogen atom since as time increases an electromagnetic field expands which would eliminate the particle structure of a hydrogen atom. Edited July 11, 2017 by ivylove
swansont Posted July 12, 2017 Posted July 12, 2017 The conjugate complex is also based on Maxwell's theory. "Denoting the conjugate complex value by a bar, this is YY*..........(28)". (Schrodinger, p. 1065). "The fluctuation of the charge will be governed by the Eq. 28, applied to the special case of the hydrogen atom. To find the radiation, that by electrodynamics will originate from these fluctuating charges, we have simply to calculate the rectangular components of the total electric moment by multiplying (28) by x, y, z respectively, then integrating over space, e.g." (Schrodinger, p. 1066). Schrodinger is using the electric field radiated by an electron to represent the structure of a hydrogen atom which is physically invalid since Maxwell's massless electromagnetic field cannot be used to represent the structure of a H atom that has a mass. Also, Maxwell's expanding electromagnetic field cannot maintain the particle structure of a hydrogen atom since as time increases an electromagnetic field expands which would eliminate the particle structure of a hydrogen atom. The wave function still doesn't have mass. There is absolutely no prohibition on having a form of equation apply to more than one phenomenon. It's not like e.g. a negative exponential only applies to radioactive decay.
ivylove Posted July 12, 2017 Author Posted July 12, 2017 Is there not a problem when a massless electromagnetic field of the wave function or conjugate complex is used to represent the structure of a H atom that has a mass.
Mordred Posted July 12, 2017 Posted July 12, 2017 (edited) Why would it? you are determining the probable location at time t of the particle property in question. In this case the energy correspondance to mass. What is invalid in applying statistical math to account for all possible locations? Gives far greater details on describing atom orbitals if you ask me. Edited July 12, 2017 by Mordred
ivylove Posted July 13, 2017 Author Posted July 13, 2017 (edited) In his paper, there is no mention of a probability of location of an electron or atomic orbitals. The wave function that represents an electric wave is being used to represent the structure of an electron that energy is being depicted with Planck's energy element (hv) but an electric field expands as time increase; therefore, a massless electric field cannot be used to represent the particle structure of an electron that has a mass. Einstein (1917) energy equation E = mc^2 is used to structurally unify Maxwell's electromagnetic field with the inertial mass (m) but E represents the energy of a massless electromagnetic wave. Furthermore, the formation of Planck's electromagnetic photon is based on a diathermic medium (ether) yet the blackbody radiation effect forms in vacuum that is void of matter which proves Planck's derivation of the energy element (hv) that is used in the depiction of Schrodinger's atomic electric wave's energies is physically invalid. Modern physicists including Einstein (1910) use Maxwell's electromagnetic field to represent an electromagnetic ether but an electromagnetic field that is propagating at the velocity of light conflicts with Fresnel's ether that remains stationary after the light wave propagates through the ether which is additional proof that Planck's energy element that is used by Schrodinger is physically invalid. Edited July 13, 2017 by ivylove
Mordred Posted July 13, 2017 Posted July 13, 2017 (edited) That relation defines the Bohr frequency potential model. The problem is that Bohr never applied elliptical orbits nor the Heisenburg uncertainty principle. These were included in later models of the atom. Part of the Schrodinger equations include the spherical harmonics based upon the particles in the box mentioned by Studiot previously. Study this chapter. https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.umich.edu/~chem461/QMChap7.pdf&ved=0ahUKEwibhrbC_oTVAhXhyoMKHSjVCOgQFggtMAQ&usg=AFQjCNGb61ArfRFhBsDYVwvvsfmRoVO8QA In particular the Schrodinger equation for orbitals 24. As well as the Born interpretation of the position equation 40. " According to Born's interpretation of the wavefunction, the probability per unit volume of finding the electron at the point (r;theta;pi) is equal to the square of the normalized wavefunction". As mentioned as well. More than 1 sentence to state what your after would be helpful. We cannot read your mind... Spend some time clarifying where your issue is with the Schrodinger equations. Don't make us guess.. (I would also study why the Schrodinger equations needed to account for the Heisenburg uncertainty on spherical harmonics.) Edited July 13, 2017 by Mordred 1
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