In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.
For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing nature.
So I am trying to understand and solve the problem mentioned in the title.I found a solution online:
https://physics.bgu.ac.il/COURSES/QuantumMechCohen/ExercisesPool/EXERCISES/ex_9011_sol_Y09.pdf
The problem is, I can't understand this step :
I relly can't find out how the two expontential...
W and Z bosons, gluons, and photons are all gauge bosons that have been found. Since the graviton can be connnected to atoms and mass in certain ways, I think that CERN may eventually prove the graviton(if real) through smashing atoms that, supposedly, have a graviton orbiting them. Could...
For t < 0 , all I can think of is a qualatative " the field is zero because the intensitity is 0 when the burst of light hasn't been emitted yet "
For t >= 0 , I've tried squaring the given E and that let's me say the amplitudes are proportional (with a cos^2 term in the mix)
But I feel like...
Cliff Notes Version
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A common topic of discussion regarding quantum mechanics is the foundations of QM as a theory structure and different interpretations of QM. These discussions are of interest to many PF members, but they present some unique challenges since they...
Has there been an experiment where 2 particles that are entangled are measured at the same time? If so what was the result?
Can any observer occupy the same frame of reference down to an electron? Don't we all exist at different times based on our frame of reference so none of us can share the...
I can't seem to wrap my head around the notion of conservation of quantum information. One thing that might help that is if someone can tell me what the associated symmetry is. For example, phase symmetry leads to conservation of electric charge according to Noether's theorem; a fact that...
Suppose the unitary operator ##e^{-\frac{i}{\hbar}\hat{H}t}## acts on ##|\psi (0) \rangle##, does it make sense for one to think of the time-evolved state as some sort of time-keeping device? If not, why? If so, is such a notion useful?
Thanks in advance!
I am searching for anything on quantum fluctuations and virtual bosons for someone who is a serious but amateur physicist ie. I have completed undergrad physics/math and some graduate level math at university. I am having a hard time finding anything that isn't beyond pop science. Not really...
Are there any research about Dark Matter missing some Hilbert space bases or observable?
Are bases or observables like spin, momentum, energy, position the basic quantum ingredients of any matter, what is the apriori explanation?
Here is my attempt at a solution. The thing I am not sure about is the final result of the Shrodinger equation and the n-values that are offered?
Did I make a math mistake?
Thank you so much for reading through this!
https://www.cnet.com/news/google-reportedly-attains-quantum-supremacy/
Google has reportedly built a quantum computer more powerful than the world's top supercomputers. A Google research paper was temporarily posted online this week, Financial Times reported Friday, and said the quantum...
Is classical physics independent from quantum physics?
Or is classical physics an approximation derived from quantum physics?
Is it dependent on interpretations? What quantum interpretations support the latter above?
Elementary question: Is there ever a case where the solutions for a wave equation turn out not to be a vector (in Hilbert space of infinite complex-valued dimensions, or a restriction to a subspace thereof) , but something else -- say, (higher-order) tensors or bivectors, or some such?
My...
Why two bodies are related with each other despite the distance between them. It is unbelievable that entanglement exist regardless of any distance. Why on universe are so deeply connected with each other where distance does not play any role for the phenomena?
Sorry in advance if this question doesn't make sense.
Anyway, I am reading a paper about quantum field theory and the Whitman Axioms (http://users.ox.ac.uk/~mert2060/GeomQuant/Wightman-Axioms.pdf), and it describes a field (Ψ) as
Ψ:𝑀→𝑉⊗End(𝐷)
where 𝑀 is a spacetime manifold, 𝑉 is a vector...
The below experimental setup is of the sort one finds frequently discussed in the delayed choice quantum eraser (QE) experiments, such as that of Kim et al. (https://arxiv.org/abs/quant-ph/9903047) I extracted only the essential part I'm wondering about and did not find a satisfying answer in...
[Edit 23.12.2019: A much extended, polished version of my contributions to this thread can be found in my paper Born's rule and measurement (arXiv:1912.09906).]
Well, it is simpler than to introduce in full generality Born's rule.
Everything can be motivated and introduced nicely for a qubit...
I am building an SF universe. While it is very similar to ours, but casual FTL exists. I don't think Lorentz transformations shouldn't work at all, but rather extra dimensions can somehow circumvent them. One kind of FTL is direct communication through entanglement.
There can be two version of...
In the paper below I've seen a new method to solve the quantum harmonic oscillator
Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve
It is done using the concept of quasi momentum defined as
$$p = - i \frac{d(\log \psi)}{dx}$$
See pg 7,8
Is this well know? is it discussed...
I have a single technical question regarding a statement on page 7 of the paper "Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence". The paper up until page 7 defines a general correlation function ##\mathcal{G}## of a basic quantum Ising...
Summary: CordFriebe et al. Has anybody read this book?
I am wading through this tome for the second time. Was wondering what others whom might have read it thought.
https://www.amazon.com/dp/3319783548/?tag=pfamazon01-20
https://www.popularmechanics.com/military/a28818232/quantum-radar/
https://www.asiatimes.com/2019/09/article/stealth-killer-quantum-radar-actually-works/?_=3274804
I don't know, whether the above sources are reliable, or not, that is why i ask.
"Quantum radars involve pairing photon particles...
I'm looking for a book that describes the quantum field theory without going deeply in the theory with formulas or complex description of the mathematics under the theory.
I know that this theory is really complex and it needs a deep knowledge of quantum physics in order to be understood.
But...
Dear PF community, I am back with a question :)
The solutions for the quantum harmonic oscillator can be found by solving the Schrödinger's equation with:
Hψ = -hbar/2m d²/dx² ψ + ½mω²x² ψ = Eψ
Solving the differential equation with ψ=C exp(-αx²/2)
gives:
-hbar/2m (-α + α²x²)ψ + ½mω²x²ψ = Eψ...
In the Kim's experiments (see picture below) part of the downwards photons are involved in a quantum eraser and part aren't.
In D0 (upward path) we see interference if the entangled photons (downward path) are detected in D1 or D2 and we don't see interference if the entangled photons are...
Hi,
I'm reading Demystifier's article about an interpretation of quantum mechanics. One concept that seems important for this interpretation is that of what is perceptible by us human beings compared to what is not (non-perceptible).
Demystifier says: A perception by a naked eye is direct, a...
I would like to apply a General Lorentz Boost to some Multi-partite Quantum State.
I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying this theory to concrete examples.
Let us take a ##|\Phi^+\rangle## Bell State as an example, and...
The wave function described seems impossible. Wave functions have to be differentiable at all points, right? Otherwise they don't represent a physically realizable state. The wave function in the example isn't differentiable at x=A, the maximum point. Also, for problem (c), I know it's visually...
I have a Hamiltonian ##H_{\lambda(t)}##, where ##\lambda (t)## characterizes a time dependent path in parameter space. The parameter is changed in finite time from ##\lambda (t_i)## to ##\lambda(t_f)## . At ##t = t_i## the system is in the intial state ##|\Psi>##. What is the work done on the...
What causes quantum uncertainty? My friend who's working for Apknite says that detectors are not the cause of wave collapse, because you are measuring something that isn't remaining in the same state.
I'm trying to understand the comment by bhobba below from another thread. A related followup from RUTA is provided for reference. After reviewing these I still don't understand. If I think in terms of a single-world (not Everette) and assume Alice and Bob are free to adjust their SG...
If I calculate ## <\psi^0|\epsilon|\psi^0>## and ## <\psi^0|-\epsilon|\psi^0>## separately and then add, the correction seems to be 0 since ##\epsilon## is a constant perturbation term.
SO how should I approach this? And how the Δ is relevant in this calculation?
Hello everybody!
I have a problem with this exercise when I have to find the possible angular momentum.
Since ##\rho^0 \rho^0## are two identical bosons, their wave function must be symmetric under exchange.
$$(exchange)\psi_{\rho\rho} = (exchange) \psi_{space} \psi_{isospin} \psi_{spin} =...
I am 3rd year physics student (actually I have just finished it). I have good knowledge on basics of quantum mechanics: I had 1 semester of Introduction to Quantum Physics and then 2 semesters of Quantum Physics. Our literature were Griffiths (Introduction to Quantum Mechanics) and ''Gennaro...
In quantum field theory, a dressed particle is a particle ("bare particle") considered in combination with certain secondary effects that it produces (e.g. the virtual pair creation involved in vacuum polarization). The dressed states are regarded as more physical, hence closer to reality.
Axel...
The book uses ladder operators ##L_+## and ##L_-## to find the eigenvalues ##m## of ##L_z##. By first deducing that these operators raise or lower the eigenvalue by ##\hbar##, and then deducing that the lowest eigenvalue is the negative of the highest eigenvalue ##l##, it proves that ##m = -l...
According to general relativity, gravity is simply the side-effect of bending the geometry of space-time. As a thought experiment imagine a 3D image being projected from a 2D hologram - the distance between the actual 2D pixels in the 2D plane always remains constant, yet depending on the shape...
I've decided to focus my essay on quantum locking: including superconductors (YBCO), the Meissner Effect. I have access to the materials needed to experiment with this topic (materials from quantumlevitation.com). Could anyone help me formulate an appropriate research question for my Extended...
Hello,
I'm considering taking the graduate level quantum mechanics course offered at my university (based on Sakurai/Shankar). I am currently reading Sakurai's QM, and mostly understand the topics (I'm currently reading the theory of angular momentum). There have been some steps where I still...
Problem Statement: Given in the "Attempt at a solution section".
Relevant Equations: Given in the "Attempt at a solution section".
Problem Statement: Given in the "Attempt at a solution section".
Relevant Equations: Given in the "Attempt at a solution section".
I am having some serious...
Richard Feynman formulated quantum path integrals to show that a single photon can theoretically travel infinitely many different paths from one point to another. The shortest path, minimizing the Lagrangian, is the one most often traveled. But certainly other paths can be taken. Using single...
I'm reading Tim Maudlin latest book "Philosophy of Physics: Quantum Theory". In the following descriptions, it is not akin to holographic?
"In the context of the quantum recipe, the mathematics of the wavefunction suggests that the quantum state (whatever it is) is a
fundamentally global sort...