Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the ...

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944 views

Differences of behaviour of a particle in a box in quantum theory between that in classic physics

Can anyone help me enlist 3 major differences between the quantum and classical physics of the behaviour of a particle in a box? I would like some insight into the differences without solving PDEs ...
2
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2answers
191 views

A universe of angular momentum?

I read this on Wikipedia: [...] That most tangible way of expressing the essence of quantum mechanics is that we live in a universe of quantized angular momentum and the Planck constant is the ...
3
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1answer
169 views

A Book about the Bohr-Einstein debate?

A book about the Bohr-Einstein debate? Is there any book that details the correspondence between the two? The only books I could find are popular science books, I wonder if there is a book that lists ...
5
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3answers
289 views

Does a ball thrown in the air really stop at its apex, and if it does, wouldn't that violate the uncertainty principle?

When throwing a ball straight up, most experts say that it momentarily comes to a stop at its apex before its return fall. If it stops, wouldn't we know its velocity and position and wouldn't this ...
3
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2answers
244 views

Can string theory be used to solve basic quantum problems?

When I studied physics I was shown that special relativity would become Newton's laws at low speeds. Similarly, quantum mechanics could also be shown to be Newtonian at large quantum numbers. My ...
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2answers
2k views

Derivatives of operators

How do derivatives of operators work? Do they act on the terms in the derivative or do they just get "added to the tail"? Is there a conceptual way to understand this? For example: say you had the ...
7
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0answers
133 views

Can we excite a nucleus by means of very intense low energy gamma-photon irradiation?

The phenomenon of multi-photon ionization of atoms has been studied, both theoretically and experimentally, for several decades. Intense laser beam devices are the apparatuses used for the ...
7
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4answers
3k views

Reading Paul Dirac's “Principles of Quantum Mechanics”

I have a similair question to the question here, but regarding a different book. "Principles of Quantum Mechanics" is a 1930 work by British Nobel laureate Paul Dirac. The wikipedia article on this ...
4
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5answers
3k views

How can the nucleus of an atom be in an excited state?

An example of the nucleus of an atom being in an excited state is the Hoyle State, which was a theory devised by the Astronomer Fred Hoyle to help describe the vast quantities of carbon-12 present in ...
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1answer
633 views

Evaluate Commutator with Partial Derivatives

I need to evaluate the following commutator... $[x(\frac{\partial}{\partial y})-y(\frac{\partial}{\partial x}),y(\frac{\partial}{\partial z})-z(\frac{\partial}{\partial y})]$ i tried applying an ...
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1answer
732 views

Differences between orthogonality and Kronecker delta function? [closed]

If $i$ and $j$ are two variables then Kronecker delta is written as $$\delta_{i,j}~:=~\begin{cases}1 \hspace{3mm} \mbox{if} \hspace{3mm} i=j,\\ 0 \hspace{3mm}\mbox{if} \hspace{3mm}i \neq ...
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2answers
653 views

Wavefunction restrictions of odd potentials

So I was just reading back through Griffiths' "Introduction to Quantum Mechanics" and solving some of the problems for practice. There is a nice one (problem 2.1c for those playing at home) where you ...
0
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1answer
425 views

Weird integration of gaussian wave packet

I have been learning Fourier transformation of a gaussian wave packet and i don't know how to calculate this integral: In the above integral we try to calculate $\varphi(\alpha)$ where $\alpha$ is ...
4
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2answers
2k views

How to apply a Hadamard gate?

How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
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1answer
245 views

What does it mean for something to be a ket?

Ok so I will provide the following example, which I am choosing at random from Sabio et al(2010): $$\psi(r,\phi)~=~\left[ \begin{array}{c} A_1r\sin(\theta-\phi)\\ ...
0
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1answer
606 views

Fourier transform between $x$ and $p$

On this page right at the top they mention two sets of fourier transform. First set is connection between $x$ (position) and $k$ (wave vector) space: $$ \begin{split} f(x) &= ...
0
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2answers
4k views

How to evaluate commutator with angular momentum? [closed]

I need to evaluate the commutator $[\hat{x},\hat{L}_z]$. I believe the $L_z$ is referring to the angular momentum operator which is: $L_z = xp_y - yp_x$ using this relationship i end up with: ...
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2answers
3k views

How to evaluate commutators?

I need to evaluate $[1/x, p]$. Note: the $p$ is the momentum operator. So far this is what i have: $$= (1/x)(p) - (p)(1/x)$$ $$= (1/x)(-ih*d/dx)-(-ih*d/dx)(1/x)$$ Ii then factor out $-ih$ to get... ...
3
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1answer
475 views

The effect of Quantum Decoherence on density operators

Suppose we have a qubit in state $| \Psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$ Suppose we expose this to decoherence, which we will express as the state $| R \rangle$ such that $$| 0 ...
2
votes
3answers
852 views

How would a Lagrangian be used to recover the Schrodinger equation?

I heard that the Lagrangian is defined in the path integral formulation of quantum mechanics. How would the Lagrangian in this formulation be used to recover the Schrodinger equation that we normally ...
3
votes
2answers
255 views

Sum of two density matrices: $\rho=p_1\rho_1+p_2\rho_2$

Suppose we have $$\rho=p_1\rho_1+p_2\rho_2$$ Where $\rho_1$ and $\rho_2$ are density matrices with $p_1+p_2=1$ I'm trying to show this is also a density matrix If we let $$\rho_1=\sum_i^n ...
1
vote
2answers
365 views

Spin of a particle and spin quantum number [duplicate]

what actually does the spin quantum number of a particle describe about? What it means when we say photon has spin 1, Higgs boson has spin 0, etc..?? What actually does that numerical value explain? I ...
1
vote
1answer
229 views

Interaction potential analysis from $\phi^4$ model

In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by $$S=\int d^d\! x ...
5
votes
2answers
269 views

Dealing with environment in a CHSH game

I am reading arxiv:1209.0448. I understand that my questions could be highly trivial. I would appreciate if anyone helps me to resolve my confusions. In a CHSH game, Alice and Bob cannot have ...
5
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2answers
298 views

Correlation, Time Ordering, and Observables

In general, the product of two Hermitian operators $\phi$ will not be Hermitian, unless the two operators commute. Question: is $X = T \phi(t_1) \phi(t_2)$ Hermitian? It doesn't seem to be if $T ...
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1answer
1k views

Wave function and Dirac bra-ket notation

Would anyone be able to explain the difference, technically, between wave function notation for quantum systems e.g. $\psi=\psi(x)$ and Dirac bra-ket vector notation? How do you get from one to the ...
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4answers
1k views

Could all strings be one single string which weaves the fabric of the universe?

This question popped out of another discussion, about if the photon needs a receiver to exist. Can a photon get emitted without a receiver? A universe containing only one electron was hypothetically ...
0
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2answers
442 views

For 2 electrons in a simple harmonic oscillator (SHO) potential, is $\langle x^2\rangle$ the same as $\langle(x_2 - x_1)^2\rangle$?

We're dealing with 2 electrons in a simple harmonic oscillator (SHO) potential. We're given the creation and annihilation operators as well as the position operator and I have to find the expectation ...
3
votes
1answer
159 views

Mathematically, how do we deduce that angular momentum is bounded?

So, how do we know $J_{+}|j,(m=j)\rangle =|0\rangle$? I.e. that m is bounded by j. We know that $J_{+}|j,(m=j)\rangle =C|j, j+1\rangle$, but how do I know that gives zero? Is it by looking at its ...
4
votes
2answers
787 views

Heisenberg uncertainty principle derivation - unexplained factor of $4 \sigma_k^2$ in Gaussian

I did a Fourier transform of a gaussian function $\scriptsize \mathcal{G}(k) = A \exp\left[-\frac{(k-k_0)^2}{2 {\sigma_k}^2}\right]$ $$ \scriptsize \begin{split} \mathcal{F}(x) &= ...
2
votes
2answers
511 views

Two ways to form SU(2) singlets?

I am trying to reconcile the two ways of forming SU(2) singlets out of a pair of doublets. Method (1): If $v=\begin{pmatrix}v^1\\ v^2\end{pmatrix}$ and $w=\begin{pmatrix}w^1\\ w^2\end{pmatrix}$ are ...
1
vote
1answer
405 views

Two Qubit problem

A two-qubit system was originally in the state $ \frac{3}{4}|00\rangle-\frac{\sqrt{5}}{4}|01\rangle+\frac{1}{4}|10\rangle-\frac{1}{4}|11\rangle $ , and then we measured the first qubit to ...
5
votes
3answers
544 views

Schrodinger equation in term of Fokker-Planck equation

From Wikipedia on the Fokker-Planck equation: $$\tag{1}\frac{\partial }{\partial t}f\left( x^{\prime },t\right) ~=~\int_{-\infty}^\infty dx\left( \left[ D_{1}\left( x,t\right) \frac{\partial ...
3
votes
1answer
131 views

How to tell if a complex exponential blows up

I'm following Griffiths' Introduction to Quantum Mechanics, where he's discussing the general solution to the delta-function potential problem. The solution he refers to is ...
1
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1answer
225 views

Relationship between a formal vector derivative and time evolution of an operator

I'm an undergraduate in physics, with all the lack of knowledge inherent in that. In two of my classes, my professors introduced two equations which look eerily similar. The first, from general ...
1
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2answers
469 views

What does the wavefunction of atom look like at low temperature?

I am reading an introduction material on Bose-Einstein condensation (BEC) at low temperature and it stated that when the temperature approaches zero kelvin, almost all atoms are degenerated into the ...
1
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1answer
1k views

De broglie equation

What is the de Broglie wavelength? Also, does the $\lambda$ sign in the de Broglie equation stand for the normal wavelength or the de Broglie wavelength? If $\lambda$ is the normal wavelength of a ...
4
votes
4answers
612 views

How do we show that no hidden variable theories can replace QM?

I've always hit two big stumbling blocks in conceiving of the proof or disproof of hidden variable theories as being even valid idea, let alone an answerable question... I feel I must be ...
3
votes
2answers
189 views

Reaction force in electron spin measurements

Consider the following (thought) experiment, where an electron is emitted, then deflected by a magnetic field, and then detected: Because the momentum of the electron changes when it gets ...
1
vote
1answer
203 views

Creating entanglement by measuring in a certain basis

This is one of the problems from Assignment 2 from CS191x at edx.org, so please do not post explicit answers. We have two qubits in the state |0+⟩ and we want to entangle them by performing a ...
2
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2answers
966 views

EPR-type experiments and faster-than-light communication using interference effects as signaling mechanism

I understand that faster-than-light communication is impossible when making single measurements, because the outcome of each measurement is random. However, shouldn't measurement on one side collapse ...
1
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1answer
907 views

Particles entangled after the big bang

Is that true that the big bang caused the quantum entanglement of all the particles of the universe so every particle is entangled to each other particle of the universe?
2
votes
2answers
492 views

Constructing a Toffoli gate with 2-and 1-qubit gates?

I'm looking through Nielson's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how ...
51
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9answers
5k views

Quantum Entanglement - What's the big deal?

Bearing in mind I am a layman - with no background in physics - please could someone explain what the "big deal" is with quantum entanglement? I used to think I understood it - that 2 particles, say ...
3
votes
1answer
355 views

Quantum computing problem [closed]

Suppose that a qubit is in the state $|\varphi\rangle=a|0\rangle+\sqrt{1-a^2}|1\rangle$, where $a\in[-1,1]$. If we first perform a standard basis measurement on this qubit and then perform a ...
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1answer
2k views

Gaussian wave packet

At our QM intro our professor said that we derive uncertainty principle using the integral of plane waves $\psi = \psi_0(k) e^{i(kx - \omega t)}$ over wave numbers $k$. We do it at $t=0$ hence $\psi = ...
8
votes
2answers
465 views

Should it be obvious that independent quantum states are composed by taking the tensor product?

My text introduces multi-quibt quantum states with the example of a state that can be "factored" into two (non-entangled) substates. It then goes on to suggest that it should be obvious1 that the ...
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0answers
58 views

Where do electrons get the energy to remain in orbit? [duplicate]

As we know electrons continuously revolve around the nuclus without falling in it at a high velocity beating it's force of attraction. My question is where do electrons get energy to revolve around ...
2
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2answers
72 views

Optical trapping problem

Can we make light slower by applying optical trapping (I mean applying laser beam to lower the speed of light)?
3
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1answer
234 views

In Klein-Gordon, why should infinite downwards photon cascades be possible?

Here is a simple point about the standard interpretation of the Klein-Gordon equation that for the life of me I've never been able to understand: Why would the existence of true negative energy ...