Tagged Questions
1
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0answers
6 views
what is the magnetic quadrupole operator?
To find magnetic or electrical moments in quantum theory we must calculate the expectation value of an appropriate operator. the dipoles operator are similar and is easy to find but the magnetic ...
0
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0answers
5 views
what is the magnetic quadrupole moment of a nuclei in cylenderical coordinates?
what is the magnetic quadruple moment of a nuclei in cylenderical coordinates?
the quadrupole moment of a nuclei is zero in spherical coordinates but in the cylenderical coordinates it can't be ...
2
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2answers
143 views
In quantum mechanics(QM), can we define a high-dimensional “spin” angular momentum other than the ordinary 3D one?
Inspired by my previous question Questions about angular momentum and 3-dimensional(3D) space? and another relevant question How to define angular momentum in other than three dimensions? , now I get ...
0
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0answers
80 views
Quantum uncertainty can explain the Riemann Hypothesis?
In the recent paper "Riemann Hypothesis as an Uncertainty Relation" (http://arxiv.org/abs/1304.2435) the author claims that the presence of zeros out of the critical line may lead to the violation of ...
4
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0answers
117 views
Question about the HVZ theorem
In this paper1 the authors cite the HVZ theorem2 saying that it follows from the method used by M. Reed & B. Simon without modifications; I don't really understand this point.
Is there anyone who ...
5
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2answers
157 views
A question on the existence of Dirac points in graphene?
As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2$\times$2 Hermitian matrix $H(k_x,k_y)$ has two degenerate points $K$ ...
1
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2answers
67 views
Schmidt basis: Entanglement
I do not understand how any state in Hilbert Space $\mathcal{H}=\mathcal{H}_A\otimes\mathcal{H}_B$ of dimension $\text{dim}(\mathcal{H}_A)\times\text{dim}(\mathcal{H}_B)$ can be decomposed in the ...
1
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3answers
171 views
Is a quantum system mandatory for generating true random sequence?
Is a quantum system necessary if we want to generate true random sequence? The mathematical framework used for classical mechanics doesn't involve any random value. But the mathematical framework of ...
1
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1answer
54 views
Can I prove boundedness of an operator without checking it for its whole domain?
(I don't have a direct reference so this is a little fishy and I'll delete it if nobody recognises what I'm talking about, but I though for starters I'll ask anyway)
I've heard at university that if ...
2
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1answer
110 views
Physical Significance of Operator Norm/Spectral Norm of a Quantum Operator
Is there any physical significance of operator norm/spectral norm of a hermitian operator?
6
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1answer
167 views
“An operator is hermitian”. Implications?
Alastair Rae states that there are 4 postulates of Quantum Mechanics in his text on the subject matter. The first part of his second postulate can be stated as:
Every dynamical variable may be ...
1
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1answer
151 views
What is the mathematical background needed for quantum physics? [duplicate]
I'm a computer scientist with a huge interest in mathematics. I have also recently started to develop some interest about quantum mechanics and quantum field theory. Assuming some knowledge in the ...
3
votes
1answer
318 views
Physical Significance of Fourier Transform and Uncertainty Relationships
What is the physical significance of a fourier transform?
I am interested in knowing exactly how it works when crossing over from momentum space to co ordinate space and also how we arrive at the ...
12
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1answer
370 views
Intuitive meaning of Hilbert Space formalism
I am totally confused about the Hilbert Space formalism of Quantum Mechanics. Can somebody please elaborate on the following points:
The observables are given by self-adjoint operators on the ...
2
votes
2answers
234 views
Intuition for Path Integrals and How to Evaluate Them
I'm just starting to come across path integrals in quantum field theory, and want to get the right intuition for the them from the start. The amplitude for propagation from $x_a$ to $x_b$ is typically ...
6
votes
1answer
143 views
Equivalent Representations of Clifford Algebra
I'm reviewing David Tong's excellent QFT lecture notes here and am a little confused by something he writes on page 94.
We've considered the standard chiral representation of the Clifford Algebra, ...
5
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1answer
169 views
Expectation value calculation for a weird operator
In the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups.- E weinberg
I am not being able to see one of the calculation. The author states (eqn 3.26)
$$\langle ...
1
vote
2answers
201 views
Angular Momentum Operators Non-Degenerate
Typically one writes simultaneous eigenstates of the angular momentum operators $J_3$ and $J^2$ as $|j,m\rangle$, where
$$J^2|j,m\rangle = \hbar^2 j(j+1)|j,m\rangle$$
$$J_3 |j,m\rangle = \hbar ...
4
votes
2answers
243 views
WKB method of approximation
Would it be legitimate to use the WKB approximation for a particle in a spherically symmetric Gaussian potential?
$$V(r)~=~V_0(1-e^{-r^2/a^2}).$$
I'm not sure when to use which approximation ...
2
votes
2answers
357 views
Non-Degeneracy of Eigenvalues of Number Operator for Simple Harmonic Oscillator [duplicate]
Possible Duplicate:
Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?
I'm trying to convince myself that the eigenvalues $n$ of the number operator ...
4
votes
3answers
544 views
Canonical Commutation Relations
Is it logically sound to accept the canonical commutation relation (CCR)
$$[x,p]~=~i\hbar$$
as a postulate of quantum mechanics? Or is it more correct to derive it given some form for $p$ in the ...
1
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4answers
279 views
Generalized quantum mechanics
I wonder if it's possible to discover another version of quantum theory that doesn't depend on complex numbers. We may discover a formulation of quantum mechanics using p-adic numbers, quaternions or ...
5
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3answers
250 views
Takhatajan's mathematical formulation of quantum mechanics
So I began skimming L. Takhatajan's Quantum Mechanics For Mathematicians, and saw the mathematical formulation of QM that he uses (page 51). (The PDF file is available here.)
I've only taken a basic ...
0
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0answers
111 views
Research in Quantum Physics [closed]
I am Suvankar, a student of engienering. My branch is Electrical & Electronics Engineering. Although this is a Physics oriented website, I want to know whether it is possible to do M.Sc. after ...
3
votes
3answers
305 views
Why we use $L_2$ Space In QM?
I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space ...
0
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1answer
164 views
State normalization in Dirac's formulation of quantum mechanics
Let us divide the time $T$ into $N$ segments each lasting $δt = T/N$. Then
we write $\langle q_F | e^{−iHT} |q_I \rangle = \langle q_F | e^{−iHδt} e^{−iHδt} . . . e^{−iHδt} |q_I \rangle $
Our ...
1
vote
1answer
141 views
Problem in Hamiltonian
I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation $$
\hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ ...
3
votes
1answer
187 views
Question on Sakurai's treatment of the Harmonic Oscillator:
In Section 2.3 of the second edition of Modern Quantum Mechanics (which discusses the harmonic oscillator), Sakurai derives the relation $$Na\left|n\right> = (n-1)a\left|n\right>,$$ and states ...
12
votes
4answers
565 views
Reason for the discreteness arising in quantum mechanics?
What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
4
votes
2answers
130 views
Quantum Mechanics in terms of *-algebras
I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading:
Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
3
votes
3answers
352 views
Can we have discontinuous wavefunctions in the Infinite Square well?
The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
3
votes
2answers
240 views
What are the solution spaces of Nonlinear Schrödinger equations?
As we know, the solution space of Schrödinger equation is a Hilbert space, however, what about it of Nonlinear Schrödinger equations such as $$i\partial_t\psi=-{1\over ...
2
votes
3answers
248 views
If I go to the church of the greater Hilbert space, can I have Unitary Collapse?
Actually, unitary pseudo-collapse?
Von Neuman said quantum mechanics proceeds by two processes: unitary evolution and nonunitary reduction, also now called projection, collapse and splitting.
...
1
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1answer
267 views
The Hermiticity of the Laplacian (and other operators)
Is the Laplacian operator, $\nabla^{2}$, a Hermitian operator?
Alternatively: is the matrix representation of the Laplacian Hermitian?
i.e.
$$\langle \nabla^{2} x | y \rangle = \langle x | ...
6
votes
2answers
185 views
Quantum mechanics on Cantor set?
Has quantum mechanics been studied on highly singular and/or discrete spaces? The particular space that I have in mind is (usual) Cantor set. What is the right way to formulate QM of a particle on a ...
0
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0answers
54 views
Is it possible to use the properties of quantum mechnics to develop a computer that develop mathmatical theory? [closed]
Is it possible to use the properties of quantum mechnics to develop a computer that develop mathmatical theory?
I want some reference please, because i want to get into very detailed.
Thanks in ...
2
votes
2answers
266 views
Is there an analogue of configuration space in quantum mechanics?
In classical mechanics coordinates are something a bit secondary. Having a configuration space $Q$ (manifold), coordinates enter as a mapping to $\mathbb R^n$, $q_i : Q \to \mathbb R$. The primary ...
3
votes
1answer
311 views
Quantum mechanic newbie: why complex amplitudes, why Hilbert space?
I'm just starting learning quantum mechanics by myself (2 "lectures" so far) and I was wondering
why we need to define quantum states in a complex vector space rater than a real one?
Also I was ...
3
votes
3answers
375 views
Existence of creation and annihilation operators
In a multiple particle Hilbert space (any space of any multi-particle system), is it sufficient to define creation and annihilation operators by their action (e.g. mapping an n-particle state to an ...
8
votes
1answer
331 views
Schwinger representation of operators for n-particle 2-mode symmetric states
A bosonic (i.e. permutation-symmetric) state of $n$ particles in $2$ modes can be written as a homogenous polynomial in the creation operators, that is
$$\left(c_0 \hat{a}^{\dagger n} + c_1 ...
2
votes
1answer
78 views
When does the “norm of quasi-eigenvectors” matter in calculations? For which physical results are these even used?
Which physical system in nonrelativistic quantum mechanics is actually described by a model, where the norm of the "position eigenstate" (i.e. the delta distribution as limit of vectors in the ...
3
votes
1answer
183 views
interpretation of Green function
Is there a physical interpretation of the existence of poles for a Green function? In particular how can we interpret the fact that a pole is purely real or purely imaginary? It's a general question ...
4
votes
1answer
120 views
Variational wavefunctions and “spread” of potential in quantum mechanics
A particle in a box has an energy that decreases with the size of the box. In the general case, it is often said that a variational solution for a "narrow and deep" potential is higher in energy than ...
9
votes
3answers
405 views
What areas of physics should a mathematician study to understand TQFT?
I am studying topological quantum field theory from the view point of mathematics.(axiomatic treatise) So it has no explanation about physics. I would like to know physic background of TQFT. But I ...
5
votes
2answers
574 views
Basic Question - Green's Functions in Quantum Mechanics
I am trying to learn about Green's functions as part of my graduate studies and have a rather basic question about them:
In my maths textbooks and a lot of places online, the basic Greens function G ...
8
votes
2answers
949 views
Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?
The standard treatment of the one-dimensional quantum simple harmonic oscillator (SHO) using the raising and lowering operators arrives at the countable basis of eigenstates $\{\vert n \rangle\}_{n = ...
7
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2answers
696 views
A book on quantum mechanics supported by the high-level mathematics
I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators ...
2
votes
1answer
476 views
General procedure for Clebsch-Gordan expansions
I'm wondering if the Clebsch-Gordan series generalize to any orthonormal set of basis functions? If so, how would one go about deriving an expression for an arbitrary set of basis functions (perhaps ...
4
votes
1answer
34 views
Tip of a spreading wave-packet: asymptotics beyond all orders of a saddle point expansion
This is a technical question coming from mapping of an unrelated problem onto dynamics of a non-relativistic massive particle in 1+1 dimensions. This issue is with asymptotics dominated by a term ...
1
vote
1answer
302 views
Bra space and adjoint vectors
If I'm not wrong, a bra, $ \langle \phi_n | $, can be thought as a linear functional that when applied to a ket vector, $| \phi_m \rangle$, returns a complex number; that is, the inner product it's a ...
