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Spherical coordinates are nothing to do with quantum numbers. They simply replace the 3 distance axes x,y, z by a radius and two angles, r, θ, φ, in order to locate points in space.

 

The algebra of Schrödinger's equation will obviously look different expressed in terms of  r, θ, φ from the way it looks in terms of x, y z, but for a system with a spherically symmetrical confining potential, as is the case with an electron confined by attraction towards a +ve atomic nucleus,  r, θ, φ is a better choice of coordinates for solving it. 

 

It is the solutions to this equation that lead to the three quantum numbers: n for the radial part ( r ) and l and m for the two angular parts (θ, φ).  l denotes the number of units of orbital angular momentum possessed by the electron (zero in the case of s orbitals, 1 for p, 2 for d, 3 for f, etc) and m denotes the orientation in space of these relative to one another, e.g. there are 3 p orbitals at right angles to one another.  (It is usual now to identify m as "m(l)", to distinguish it from "m(s)", which is used for the "spin" of the electron - something that does not come out of Schrödinger's equation.) 

Edited by exchemist
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The Bohr-de Broglie atomic matter wave is transformed into an electron particle-in-a-box wave that is transformed into a probability wave then represented in a spherical coordinate system to create the structural equations of the atomic orbitals but a spherical coordinate system is being used to derive the structure of an atom using the box normalized probability wave which is physically invalid since a coordinate system is a representation of a structure and cannot be used to construct a structure of an atom or molecule that is depict in the QM atomic orbital equations.

 

 

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Alright1234

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"The algebra of Schrödinger's equation will obviously look different expressed in terms of  r, θ, φ from the way it looks in terms of x, y z, but for a system with a spherically symmetrical confining potential, as is the case with an electron confined by attraction towards a +ve atomic nucleus,  r, θ, φ is a better choice of coordinates for solving it."

 

 

EXCHEM   none of this explain why a spherical coordinate system is used to represent non spherical structures of the atomic orbitals.

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I watched the video. I didn't know there was still a debate about the wave function. I thought it contained all probabilities and it wasn't your measurement that caused the collapse of the wavefunction but it was your measuring device that could only detect one of the probabilities. So you do get that multifood item but if you can only taste hotdogs, that's all you'll be able to get out of the box. That multiworlds idea just turns my stomach. 


 


So it looks like you can go around the restrictions set by quantum physics. By taking enough still shots, you can combine them to see the motion shots. That means I am wrong about how the food box analogy works. You're not limited to only tasting hotdogs. What happens is when you open enough boxes, you will be able to see what percentage of burgers, pizza and hotdogs will pop out of the multifood item.


 


That means there's now a 3rd option of wavefunction collapse. The 1st was the act of measuring that influenced the collapse into the same result as what happens in the double slit experiment. The 2nd is the type of equipment or where you placed the equipment you used to measure only allowed you to see 1 result. The 3rd is now the result is independent of the act of measurement or the equipment used but how many measurements you take. That sure isn't in my quantum physics book (which is the greatest book I ever read (A quantum story by baggot)).


 


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Dear Sir Ralfcis None of this explain why a spherical coordinate system is used to represent non spherical structures of the atomic orbitals.


 


 


Love Alright1234

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Spherical coordinates are nothing to do with quantum numbers. They simply replace the 3 distance axes x,y, z by a radius and two angles, r, θ, φ, in order to locate points in space.

 

The algebra of Schrödinger's equation will obviously look different expressed in terms of  r, θ, φ from the way it looks in terms of x, y z, but for a system with a spherically symmetrical confining potential, as is the case with an electron confined by attraction towards a +ve atomic nucleus,  r, θ, φ is a better choice of coordinates for solving it. 

 

It is the solutions to this equation that lead to the three quantum numbers: n for the radial part ( r ) and l and m for the two angular parts (θ, φ).  l denotes the number of units of orbital angular momentum possessed by the electron (zero in the case of s orbitals, 1 for p, 2 for d, 3 for f, etc) and m denotes the orientation in space of these relative to one another, e.g. there are 3 p orbitals at right angles to one another.  (It is usual now to identify m as "m(l)", to distinguish it from "m(s)", which is used for the "spin" of the electron - something that does not come out of Schrödinger's equation.) 

 Which those are called Quantum Numbers when you do that. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/quantum.html

Edited by VictorMedvil
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