230
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What is an "attosecond pulse", and what can you use it for?
What's the big deal?
When quantum mechanics was being discovered and formalized, in the 1920s and 1930s, our view of physics was deeply rooted in the macroscopic world. We understood that microscopic ...
- 135k
44
votes
What experimental proof of quantum superposition do we have?
"Being in superposition" is not an objective property of a quantum mechanical state. Quantum mechanical states live in a Hilbert space, where, since it is a vector space, every state can be ...
- 127k
38
votes
Accepted
How does spacetime curve around an object in superposition?
The short answer is we do not know.
Our best theory of gravity, general relativity, tells us that the curvature of spacetime follows Einstein's equation,
$$ G_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu},$$...
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29
votes
Accepted
Since water is a molecule, can the aerosol sprayed through double slit form interference pattern?
No, not with a spray.
The reason for this is that "sprays" are not isolated molecules. They are fine droplets, and the individual droplets are still vastly larger than a molecule - a ...
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27
votes
Accepted
Why are quantum effects of the apparatus ignored in quantum experiments?
And in all the experiments all these in-between steps are considered to be "magically perfect". Nobody pays them any more attention except to mention that they're there. All mirrors reflect ...
- 648
24
votes
On a tinted (reflective) window, why do I need to look from up close to see inside?
Things are called a one-way mirror when the amount of reflected light overwhelms the amount of transmitted light.
When you put your head up to the glass (and maybe put your hands up surrounding your ...
- 42k
23
votes
Do we understand chemistry from particle physics?
While the discoveries of the rules of chemistry and some current practical wisdom is empirical, it is better to think of the entire nature of chemistry as dictated by the principles of quantum ...
- 3,242
22
votes
How are quantum systems different from dice?
"Is a state space H
for a quantum system just a sample space in a probability space?"
No. Random variables defined on a sample space have a joint probability distribution. Quantum ...
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22
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What would one use a theory of quantum gravity for?
The two standard answers are:
Resolving the singularity at the Big Bang
Resolving the singularity in Black Holes
Both of these have large spatial curvature within very small regions.
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22
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Why are expectation values of an observable important in QM?
This is an important point which should be discussed.
What one obtains from experiments are frequencies of outcomes of given measured observables on an ensemble of identical quantum systems all ...
- 75.8k
20
votes
Accepted
Is intrinsic spin a quantum or/and a relativistic phenomenon?
SPIN ORIGIN
Spin is a purely relativistic property.
It comes in fact from the representation theory of the Lorentz group (the relativistic symmetries group).
In classical mechanics, you have ...
- 1,809
20
votes
Why do valence electrons not push each other away?
First of all, the electrons do exert a repulsive force on one another. This is inherently accounted for in the electrostatic repulsion terms in the atomic Hamiltonian that is used to solve the ...
- 3,242
19
votes
Electron "clouds" in an atom
I like this question, because it combines 3 intro-level quantum analogies that are fine for chemists, but are insufficient for physicists.
Let's start with the orbital: it is not a probability cloud. ...
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18
votes
Accepted
A better Schrödinger Equation with Relativistic Effects?
Your spectrum does not contain relativistic corrections, it is the "gross structure." It is the correct non relavistic limit (gross structure), since your equation contains Schrödinger in ...
- 13.5k
18
votes
Quantum harmonic oscillator meaning
$\hat{H}$ is an unbounded operator. It is a fact from Functional Analysis that Hermitian unbounded operators cannot be defined on the entire Hilbert space, only in subspaces of it: this result is ...
- 22.4k
17
votes
Accepted
"There is a bra for every ket, but there is not a ket for every bra"
The kets and bras do not always live in a Hilbert space, but when you write something like the "position eigenbras" $\langle x\rvert$, this lives in a larger space that is part of the Gel'...
- 127k
17
votes
Accepted
How to rotate an electron mathematically?
(I wrote this answer in a hurry yesterday, I now fixed a huge number of typos and various mistakes, sorry.)
Well, there are a number of important issues in the question.
First of all, pure quantum ...
- 75.8k
17
votes
What experimental proof of quantum superposition do we have?
I guess you might know that if you have a linear equation $\mathcal{L}$ and two solutions of it, then a superposition of these solutions is also a solution of this linear equation.
$$
\mathcal{L}(f(x))...
- 1,110
16
votes
Why do particles tend to collapse to *energy*-eigenstates (rather than some other basis)?
But energy eigenstates are just one particular basis for representing quantum states of an electron. Why do particles tend to eigenstates of the hamiltonian,
States don't "tend to" do ...
- 22.5k
16
votes
Where is the paradox in the double-slit experiment?
The reason it is "paradoxical" (probably strange, weird, would be better words as there is no paradox within the laws of quantum mechanics) is the following:
The interference pattern in the ...
- 2,484
16
votes
Exponential operator approximation: Suzuki-Trotter Expansion
Hint: Use the BCH formula multiple times:
$$ e^{tA}e^{tB}~\stackrel{\text{BCH}}{=}~e^{tA+tB+[tA,tB]/2 +{\cal O}(t^3)}~\stackrel{\text{BCH}}{=}~e^{tA+tB}e^{[tA,tB]/2}+{\cal O}(t^3),\tag{1}$$
$$ e^{tB}e^...
- 209k
15
votes
Accepted
Examples of systems with infinite dimensional Hilbert space, whose energy is bounded from above
In standard quantum mechanics, more precisely for systems described in $L^2(\mathbb{R}, dx)$ (and this generalizes to many dimensions) Hamiltonians are (selfadjoint extensions of) operators of the ...
- 75.8k
15
votes
Accepted
Property of the Hamiltonian's discrete spectrum
This is the so-called Weinstein criterion.$^1$ To prove it, we proceed as OP and expand the (normalized) vector $\psi$ into the (assumed to be) complete orthonormal eigenbasis of $H$ and denote by $...
- 8,375
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votes
Accepted
Can the collapse of the wave function be modelled as a quantum system on its own?
To model the act of measurement itself as an interaction of the measurement apparatus and the measured system as quantum systems is a perfectly standard thing to do, though you might get disagreements ...
- 127k
14
votes
Accepted
Why do particles tend to collapse to *energy*-eigenstates (rather than some other basis)?
If a system is undergoing interference and information is copied out of that system that tends to suppress the interference: this process is called decoherence. For macroscopic objects this is usually ...
- 9,308
14
votes
Can the universe be unpredictable but still have only one possible history?
Science cannot answer these questions, nor does it try to. The questions you ask are philosophical questions, so the philosophical terminology is useful. You speak of ontology: the study of what is &...
- 50.8k
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 ...
- 75.8k
13
votes
Accepted
Why don't electrons occupy infinite degenerate states with the same energy?
Pauli exclusion comes from the fact that the wave function of the $N$-electron system has to be anti-symmetric under exchange of the particle labels; this is a consequence of the fact that electrons ...
- 8,424
13
votes
Do we understand chemistry from particle physics?
atoms have 8 electron "slots" in their outer shell
The shape of the periodic table is one of the great successes of non-relativistic quantum mechanics. If we approximate that we're ...
rob♦
- 92.1k
13
votes
Accepted
Simultaneity and The Uncertainty Principle
I think you are conflating two separate issues. Lack of simultaneity in SR is an effect which increases with distance along the direction of travel between two reference frames moving relative to each ...
- 26.7k
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