Linked Questions

13
votes
3answers
3k views

Born's Rule, What is the Reason? [duplicate]

As far as I've read online, there isn't a good explanation for the Born Rule. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives ...
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 ...
1
vote
0answers
255 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, ...
1
vote
1answer
171 views

Probability in QM: derivation or interpretation? [duplicate]

It is known that coordinates $C_k\in\mathbb{C}$ of the QM-state vectors $|\psi\rangle$ has an interpretation as probability weights $p_k$ in the whole state through the formula like $|C_k|^2=p_k$. We ...
2
votes
0answers
142 views

Can the Born rule be derived? [duplicate]

$\renewcommand{ket}[1]{|#1\rangle}$ If we have a particle and we know the initial state $|\psi\rangle$ of everything that is relevant, and we know the full Hamiltonian $H$, then we should be able to ...
0
votes
1answer
98 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?
77
votes
15answers
10k views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
19
votes
10answers
2k views

On a measurement level, is quantum mechanics a deterministic theory or a probability theory?

Quantum mechanics is a non-commutative probability theory. As such, it fundamentally behaves differently from classical probability theories. This manifests itself most pronouncedly in the uncertainty ...
7
votes
4answers
2k views

How can indeterminacy in quantum mechanics be derived from lack of ability to observe a cause?

I don't get this part of quantum mechanics. I get the part that you can't observe particles and not affect their behavior because you are shooting photons to them while you are observing them, but ...
2
votes
1answer
4k views

Overlap integral and probability

I have a question regarding how to extract probability from an overlap integral. Specifically, I am calculating the probability of a particle in a bound state in a delta potential $V=-\alpha \delta(x)$...
3
votes
2answers
215 views

If a quantum state is pure why are its observables still probabilistic?

As I understand it, a pure quantum state is one that can be represented as a ket $\lvert\psi\rangle$ in a Hilbert space, and it contains all the information about the state of the system. As such, we ...
-1
votes
1answer
131 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
2answers
354 views

The irreducible observer

This question probably verges on pseudo-science and probably sounds like gibberish, so please pardon me. But I'll ask it anyway. In an ideal lab experiment there is generally a separation between the ...
1
vote
0answers
50 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 ...