# What, exactly, does Schrödinger's wave equation describe (just in plain English, without any of the math please) [closed]

I've been studying the philosophical foundations of quantum mechanics and would love to find out if my understanding is correct. Could anyone please let me know if the below description is accurate? If not accurate, could you please explain why without any math at all?

Here is what I think but not sure if correct:

In creating quantum mechanics, Schrodinger modified the classical equation of Newton's second law. In the classical equation, Schrodinger replaced the exactly determinable values for the complementary variables position and momentum with probability distributions contracting or expanding according to the uncertainty principle, representing decreasing or increasing clouds of uncertainty in one’s ability to deterministically predict either position or momentum. In Schrodinger's wave equation, the probability distributions representing clouds of uncertainty or indeterminacy are called wave functions. This is another way of stating that Schrodinger's wave equation is solvable for the wave functions instead of being solvable for the precisely determinable variables of classical physics.

Is the above accurate or not? Your help is much appreciated.

• Perhaps this will help - Does the collapse of the wave function happen immediately everywhere? Commented Jul 21 at 3:23
• The variable in the Schrodinger equation does not represent anything observable, or a probability distribution for anything observable. It represents an element of an abstract state space, which governs probability distributions for all possible observables via the Born rule. Commented Jul 21 at 3:58
• There is oddly no independent momentum variable in the Schrodinger equation; velocity is entirely encoded in the positional distribution of the wave packet. When a potential gradient V is applied, the different pulls on different parts of the wave packet ends up propelling the wave in space and give it velocity. If V is suddenly switched off (set to 0 everywhere), then the wave packet stops moving (unlike inertia of a ball). Commented Jul 21 at 5:00
• @MattHanson I think you should read the question beyond the first line. This is definitely not a question about the Philosophy of Physics but about Physics, and in particular physical concepts. Therefore is suitable for this site. The OP makes some wrong assumptions, but this site is not reserved to people with a PhD in Physics. Commented Jul 21 at 5:32
• Schrödinger was working independently of Heisenberg; there is definitely nothing about "helping" happening anywhere, and Heisenberg originally did not like Schrödinger's work at all; it took both Schrödinger and Dirac to prove equivalence different ways, in order for Heisenberg to stop complaining. And when Schrödinger first found his wave equation, he did not know that it had anything to do with probabilities. Born had to come by and convince Schrödinger about that. Commented Jul 21 at 6:17

Unfortunately, in a specific sense your description is quite wrong.

Many of the aspects that you describe are interpretations that arose years after the framework was first published.

You are attributing considerations to Schrödinger that were not on his mind at the time.

In particular, at the time Schrödinger was not considering interpretation in terms of probabilities.

Your description is at odds with the historical sequence of development of ideas. You push many years of development of ideas onto Schrödinger.

Your description of ideas about interpretation of the Schrödinger isn't necessarily wrong, but your representation of the history is definitely wrong, and in that sense your effort is badly misdirected.

It's hard to say whether its correct or not...Because its hard to say whether our understanding are the same.

For the key part of your statement

In the classical equation, Schrodinger replaced the exactly determinable values for complementary variables like position and momentum with probability distributions contracting or expanding according to the uncertainty principle, representing decreasing or increasing clouds of uncertainty in one’s ability to deterministically predict either position or momentum (or any other pair of complementary variables).

It would be much more clear if we use math,but if math is forbidden,I would like to say:maybe you're right,but I am not certainly sure.

I strongly suggest you read a QM book.Even may you cant fully accept its math,you may have a more clear understanding.

No, the wavefunction is not the probability of finding the particle at some location, rather, the probability is something similar to the square of the wavefunction, but a little more complicated. So the wavefunction is not the square root of the probability, but a little more complicated. But once you have the wavefunction you can get the probability.

All info is on the wavefunction, with extra manipulations you can use it to calculate the probability of measuring any other physical quantity, such as energy or momentum, not only position