Linked Questions

15
votes
7answers
2k views

Born rule and unitary evolution

Is the Born rule a fundamental postulate of quantum mechanics, or can it be inferred from unitary evolution?
2
votes
0answers
393 views

Probability and probability amplitude [duplicate]

What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
1
vote
0answers
269 views

Why must the probability be the integrated square modulus of the wave function [duplicate]

Quantum mechanics uses the wave function to calculate probabilities by taking the square modulus of the wave function as requirement by Max Born. Why should this (squaring of the wave function) be so, ...
0
votes
1answer
100 views

Where does the postulate of quantum mechanic that possible results are eigenvalues come from? [duplicate]

Where does the idea come from, that possible results of quantum measurement are eigenvalues of the operator corresponding to the observable?
2
votes
3answers
4k views

Why is $|\Psi|^2$ the probability density?

I am starting with Quantum Mechanics, learning online. I can't seem to find the reason for $|\Psi|^2$ being the probability density of finding an electron. They've just taken it for granted everywhere....
8
votes
3answers
921 views

Could quantum mechanics work without the Born rule?

Slightly inspired by this question about the historical origins of the Born rule, I wondered whether quantum mechanics could still work without the Born rule. I realize it's one of the most ...
4
votes
2answers
3k views

Why does the magnitude squared of the wave function give us the probability density? [duplicate]

My question doesn't go much beyond the title: Why does $$\left | \psi \left ( x,t \right ) \right |^{2}$$ give us the probability density of something appearing at a certain location? I understand ...
9
votes
4answers
533 views

Is there a mathematical basis for Born rule?

Wave function determines complex amplitudes to possible measurement outcomes. The Born Rule states that the probability of obtaining some measurement outcome is equal to the square of the ...
3
votes
2answers
336 views

Are probability-preserving variations of QT with respect to the Born rule mathematically possible?

Is it possible to create (m)any theoretically workable framework(s) - that do(es) produce probabilities - by taking QM and replacing the Born(-like) rule(s) with something that is not equivalent to it ...
-1
votes
1answer
132 views

Does the Born rule imply $L_2$ Space?

I see no formal proof of the Born rule. Well, the normalizing condition $\int_\infty|\Psi|^2dx=1$ is because of Born rule if I am not wrong. Does this imply that our reality is a $L_2$ space? If ...
0
votes
0answers
492 views

Why do we square probability amplitude? Why not direct values?

According to my knowledge (which is feeble) we will also get the same result if used direct values. For example, if the probability of something happening is 4% or 0.04, we should make an arrow of 0....
2
votes
0answers
96 views

Measure-theoretic maths behind Born's probabilistic interpretation of Schrodinger's equation

I was reading a bit about Quantum Mechanics, Schrodinger's equation and its probabilistic interpretation (found this very insightful intro here https://plus.maths.org/content/schrodinger-1), my ...
1
vote
0answers
51 views

Validity of analysing spherical harmonics in real-space using the probability amplitude [closed]

While looking up spherical harmonics (on the validity of analysing them in real-space in a transition metal crystal structure), I came across this: http://shpenkov.janmax.com/hybridizationshpenkov.pdf ...