Probability in quantum mechanics

[Cheman]

When you calculate the probability of an electron being somewhere, eg in the case of orbitals, is the result in the form eg 1/2 or 50%, 1/4 or 25%, etc? Or is it of some other form?

Thanks.

 

[dextercioby]

When you calculate the probability of an electron being somewhere, eg in the case of orbitals, is the result in the form eg 1/2 or 50%, 1/4 or 25%, etc? Or is it of some other form?

Thanks.

Probabilities are defines as numbers in the interval [0,1],for any situation.And those in QM cannot make an exception.However,noone can prevent you to express a probability of,let's say 1/3,in terms of procents as :33,(3) %;

Daniel.

 

[jtbell]

Note, however, if Cheman is thinking of the quantity $$\psi^*(x) \psi (x)$$, that is the probability density, not the probability. It's not limited to a maximum value of 1, although the minimum is still 0.

When you integrate the probability density over some region, to get the probability of the particle being in that region,

$$\int_{a}^{b} \psi^* (x) \psi (x) dx$$

then you should get a number between 0 and 1, if $$\psi (x)$$ is normalized so that

$$\int_{-\infty}^{+\infty} \psi^* (x) \psi (x) dx = 1$$

 

[dextercioby]

Note, however, if Cheman is thinking of the quantity $$\psi^*(x) \psi (x)$$, that is the probability density, not the probability. It's not limited to a maximum value of 1, although the minimum is still 0.

When you integrate the probability density over some region, to get the probability of the particle being in that region,

$$\int_{a}^{b} \psi^* (x) \psi (x) dx$$

then you should get a number between 0 and 1, if $$\psi (x)$$ is normalized so that

$$\int_{-\infty}^{+\infty} \psi^* (x) \psi (x) dx = 1$$

When you calculate the probability of an electron being somewhere, eg in the case of orbitals, is the result in the form eg 1/2 or 50%, 1/4 or 25%, etc? Or is it of some other form?

HE ASKED ABOUT PROBABILITIES,HAD HE ASKED ABOUT PROBABILIY DENSITIES,MY ANSWER WOULD HAVE BEEN DIFFERENT.

Why did u undrestand differently?

 

[RedX]

When you calculate the probability of an electron being somewhere, eg in the case of orbitals, is the result in the form eg 1/2 or 50%, 1/4 or 25%, etc? Or is it of some other form?

Thanks.

Yeah, but generally that's a question of statistical physics and not quantum mechanics. Statistical physics says most often the atom would be in the lowest energy state, so the electron most likely occupies the lowest energy level (particularly since electron energies are so huge (compared to for instance vibrational energies) that it's very unlikely that you'd find the electron not in the ground state). Given the wavefunction of the electron you can calculate the probabilities that the electron is in a certain orbital. But that's not really how it works in practice.

 

[jtbell]

HE ASKED ABOUT PROBABILITIES,HAD HE ASKED ABOUT PROBABILIY DENSITIES,MY ANSWER WOULD HAVE BEEN DIFFERENT.

Why did u undrestand differently?

I've seen beginning students in QM get confused about the difference between probability density and probability, or get careless and say "probability" when they really mean "probability density." I figured if he was confused about what kind of numbers come out of it, he might very well be confused about the whole concept.

Sometimes the question that gets asked isn't the one that really needs answering.

 

[dextercioby]

I've seen beginning students in QM get confused about the difference between probability density and probability, or get careless and say "probability" when they really mean "probability density." I figured if he was confused about what kind of numbers come out of it, he might very well be confused about the whole concept.

Sometimes the question that gets asked isn't the one that really needs answering.

Then u must be one heck of a mind reader. For this type of exercise,i cannot go beyond the words that are stated and appear on the screen in front of my very eyes.So i cannot make predictions about what he really meant,and therefore i have to answer the posted question,not what i'd like to answer.
One the other hand,u may be right.Students (good ones,the ones who really care) tend to mix several concepts in QM (especially the ones dealing with the fundamental interpretation,the statistical one) because it's either they lack training with statistical concepts (dealt in a separate course on methods of mathematics for physics,for example),or the QM teacher/book is that bad as not to get u straight with the difference between a function (an application from one set to another) and a number (an element of a set).
And that's really bad...

Daniel.

 

[Doc Al]

We really need to calm down here folks!

Daniel: Nothing that jtbell said contradicted anything you had posted. He was just adding a little more to the thread by clarifying something that Cheman may well need clarified. (Perhaps we'll never know! )

 

[DaveC426913]

"Sometimes the question that gets asked isn't the one that really needs answering."

This is absolutely true, and is what separates a good teacher/tutor from someone who merely points you at the chapter review in the textbook. The time you learn the most is when you discover that you don't *know* what you don't know.

And yes, good teachers are usually good mind readers.

 

[Louis Cypher]

He's hit the nail on the head here, a good tutor will ask you to read something a great tutor will ask you to come up with a better idea, thought about accepted ideas, is proper science, after all when Plank Einstein etc questioned Newton Qm and realtivity was born, Einstein questioned qm with his god doesn't play dice, an international forum of QM's antagonists and QM's Protaginists lead by Schrödinger eventually won the nay sayers over, this is science, read don't necessarily accept, proof is key but though is the key to proof Schrödinger new there were problems with QM his only regret was that he wouldn't be alive to see his child disproven, maybe we will?

 

[godzilla7]

Like that quote about science being a series of deaths