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13 votes

Is the zero vector necessary to do quantum mechanics?

Quantum theory can be completely stated in the complex projective space of a complex Hilbert space. The basic object from this perspective is the transition probability of a couple of rays (pure ...
Valter Moretti's user avatar
10 votes

Physical meaning of each term of the square modulus of a wave function

1 - The cross term $\psi_0\psi_1\cos(\omega t)$ can be interpreted as an interference term of the states $\psi_0$ and $\psi_0$, which importantly depends on time, as these states have different ...
Gabriel Ybarra Marcaida's user avatar
8 votes
Accepted

What Does Feynman Mean When He Says Amplitude and Probabilities?

I think the confusion starts from an interpretation of quantum mechanics I have seen many times applied to atomic orbitals or Young's double-slit experiment (YDSE). In the former case the electron has ...
JEB's user avatar
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2 votes
Accepted

Quantum Mechanical Current Normalisation

Well, the Schroedinger equation for $\psi$ is always kind of the same; the potential energy or the number of kinetic terms changes, but otherwise the form $$ \hat{H}\psi = E\psi $$ remains. But the ...
Ján Lalinský's user avatar
2 votes

What Does Feynman Mean When He Says Amplitude and Probabilities?

I believe your interpretation of Feynman is fully correct here. He is drawing a line between which objects in the theory need to have wavefunctions (amplitudes) and which can be described by ordinary ...
Dast's user avatar
  • 1,836
2 votes

Is the zero vector necessary to do quantum mechanics?

This is largely a philosophical question, but I would argue that yes, the zero vector is necessary for QM to make sense conceptually. A few examples (off the top of my head) of places where the zero ...
tparker's user avatar
  • 48.3k
1 vote

Quantum Mechanical Current Normalisation

You just need to normalise your solution to unity, after correcting your expressions. The meaning of this is known as the Born rule.
my2cts's user avatar
  • 25.3k
1 vote

Quantum: Which improbable macroscopic events are possible?

In quantum theory the different possible values of a measurable quantity can interfere with one another. The state of any object including the keyboard on which I am typing this isn't perfectly ...
alanf's user avatar
  • 8,504
1 vote

Quantum: Which improbable macroscopic events are possible?

What follows is an intuitive answer (i.e. it is low on rigour). The informal (and slightly satirical) totalitarian principle states that any process that doesn't violate a finite number of ...
Martin C.'s user avatar
  • 1,471
1 vote

Probabilistic behavior of quantum mechanics

If you have two identically prepared systems, say two copies of the state $ \alpha \vert \uparrow \rangle + \beta \vert \downarrow\rangle$, with $\vert \alpha\vert^2+\vert\beta\vert^2=1$, you might ...
ZeroTheHero's user avatar
  • 46.1k
1 vote

Factorization on increments in Markov chain

I doubt that the statement you want to prove is generally true for any Markov process. Note that \begin{align} & \left<x(t+\tau)-x(t)\right>\left<x(t'+\tau)-x(t')\right> = \\ &\...
Javi's user avatar
  • 1,091
1 vote
Accepted

Boltzmann distributions on atomic orbitals: infinite degeneracy?

Obviously, my reasoning is faulty, as it predicts all atoms to be ionized at all times, but that's not what we observe. I've been told that this is all due to interference from other (nearby) atoms, ...
Ján Lalinský's user avatar

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