swansont

A behavior you have admitted to not studying and having no expertise in understanding. Analogies are limited in usefulness. Analogies of quantum systems are typically more limited. Again, it’s preferable to actually discuss QM.

Also, how many legs did the individuals in the control group have? (and were these in vivo tests?)

Designed to be? Any evidence to support these rather sexist claims? Repeating a claim is not evidence

The 1S wave function varies as e^-r/a, which is not proportional to the electrostatic PE

Meanwhile you are still not a quantum particle. The physics of your behavior is quite adequately described by classical physics, and this is still not relevant to the topic of the thread.

And? You need to include the part where you explain how this has relevance Not clear what your position is. So this, too, is irrelevant to the topic. That’s not what I said, so I don’t know what prompts this question. Reading comprehension issues? Rule 2.5 Stay on topic. Posts should be relevant to the discussion at hand. This means that you shouldn't use scientific threads to advertise your own personal theory, or post only to incite a hostile argument.

I don’t see how that’s relevant to the topic. You can look at the graph (or equation) of the probability density for various n levels and compare. If you have questions about it you should ask. You perhaps overestimate how much I keep track of others’ backgrounds. If you want to discuss QM, and especially if you assert that it works a certain way, I assume a certain level of familiarity. If that’s lacking, then this is a waste of time; you can’t build a proper model or assess criticism of your idea. The topic here is the electron’s wave function and probability density. Tying in to other speculative ideas is against the rules.

Not really. You are not a quantum particle, and location isn’t a property that has a quantum number. Can we deal with actual QM and not analogies? That removes much of the ambiguity. Answered. It’s because of the math, both “this is what the math is” and “because you’re using spherical coordinates”; the volume element depends on the radius. The probability density isn’t the quantity with physical meaning, so there isn’t a physical justification I can give. Answers get merged. And if I edit immediately, I usually don’t annotate it.

And yet what you wrote is in agreement with what I wrote regarding the PEP No, there is nobody identical to you. In hydrogenoid atoms, the energy of an orbital is only a function of its main quantum number, n, which means that all the orbitals of the same shell will have the same energy. In a single-electron atom, an electron in a 2s orbital will have exactly the same energy as an electron in a 2p orbital, because they only interact with the nucleus through a Coulombic interaction Citation? You quote something, you need to provide a link. There’s probably something that says this is what’s predicted by the Schrödinger equation. This turns out to not be true, once you delve a little deeper into quantum physics. It’s called the Lamb shift. https://en.wikipedia.org/wiki/Lamb_shift This also ignores the hyperfine splitting, where the spin of the electron matters in determining the energy.

“all due respect” usually indicates disagreement. One of the components of the PEP is that you have identical particles, as I indicated. If they are unique they aren’t identical. If it’s on “another shell” then there is some difference in its state (whatever you mean by A or 1; we do have actual physics terminology we could use) e.g. an electron in n=2 and the s state, can be spin up, and also have an electron in n=3, s state that is spin up. Such as you’d find in Ar. “on the left” really has no meaning in this context.

If electrons were unique they wouldn’t end up in all these different states. It’s because they are identical that they need to be in different n, l or m states to satisfy the Pauli exclusion principle

What I said conveys pretty much the same information about hyperfine structure as the quote you provided, so yes. Why do you ask?

Some quantum particles, like electrons and protons, behave like little magnets, owing to having a charge and intrinsic angular momentum (spin). So a “spin up” electron will have a different energy than “spin down” in the presence of a magnetic field, which is provided by the nucleus. This energy splitting is the hyperfine splitting.

! Moderator Note “Do better” does not mean “post the same drivel in another inappropriate section of the forum” We’re a science forum, which means science discussion, not an economics blog post

What are these layers you are referring to?

Of course density has a physical meaning, since you would typically have a volume of the material. The question here was the probability at the origin as well as nearby. The volume element depends on the surface area of the shell, so it’s smaller close to the origin, and zero at the origin, and this artifact of the math has to be included when discussing the significance of the wave function’s value. The nucleus has a physical size, so sure. The electron interacts electromagnetically and the fact the the electron can be found there accounts for the large hyperfine splitting of the s state as opposed to the p states, where the wave function has a node, and so doesn’t have nearly as strong an interaction. In alkali atoms the hyperfine splitting of the ground state is hundreds of MHz to >1 GHz, while the excited p-state is significantly smaller

But if it’s zero, are you considering a volume? How much mass do you have in zero volume, regardless of the density?

If you’re going to posit a civilization that is on the cusp of being technologically capable of interstellar travel, it seems reasonable to assume they are capable of solving solvable problems like global warming and population, which are more political in nature (i.e. it’s about the will to solve the problem, not the means)

To the extent that “a sphere with zero volume” is meaningful, yes. But also that probability density lacks physical meaning if you ignore the volume you’re looking at.

There’s a mundane mathematical aspect to it. In a 1D system in cartesian coordinates, the square of the wave function gives us a probability. But going to 3D this is a density, so the probability is not just the square of the wave function. And we’ve moved to a spherical coordinate system. The volume element integral includes r^2dr, instead of the dx we had before. If you solved for a 1/x potential in cartesian coordinates, you’re going to get a wave function that looks something like xe^-x/a (for x>0), i.e. something that goes to zero at the origin

This also explains the relatively large hyperfine splitting of the S state. That’s the solution to the Schrödinger equation. This has to be multiplied by the volume element, which depends on r and is zero at r=0, to get the physically meaningful quantity.

It isn’t. You might have only been looking at the wave function itself. The probability multiplies this by r^2, making it go to zero at the origin. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydr.html

Yes, it’s a mathematical consequence, because the equation that describes the probability is math. Quantum mechanics can be hard to conceptualize, as some ideas are at odds with classical, everyday notions. Such as the electron having some particle behaviors and some wave behaviors, and the way probability shows up in the way things work. The hydrogen radial wave function drops off as e^-r/a (and probability is the square of that) so while there is a probability of finding the electron far from the nucleus it is vanishingly small.

A whistle-blower is one who reports wrongdoing to their chain of command or a designated point of contact outside the chain. There’s nothing traitorous about reporting suspected criminal behavior to the authorities.

Which would have been fine in a thread on alternative power, but not in science news, which need to focus on the linked article