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4answers
378 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 ...
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1answer
230 views

Equivalent system in Centre manifold theory

I was studying the centre manifold theory. It says (see Kuznetsov page 155, theorem 5.2) that the system on the left side of the picture is topologically equivalent to the one on the right. $ ...
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1answer
539 views

What is the mathematical nature of space time quantization in string theory/super string theory?

I don't know much about string theory, apart from it being a theory of everything which brings QM, QED and nuclear forces and gravity under one single roof. I am curious to know from a mathematical ...
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1answer
52 views

Description of charged sphere with Heaviside function in cylindrical coordinates

I need to describe density of charge of uniformly charged sphere (radius R, total charge Q, position of centre (0,0,0)) with Dirac delta function and Heaviside step function. The hard part is to ...
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3answers
115 views

Can one construct a new operator in terms of the powers of another operator?

Suppose we have a quantum state, well described by its time-independent wave function Psi. And we have a well-defined Hermitian (self-adjoint) operator $A$. We successfully evaluate the expectation ...
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2answers
233 views

Separation of variables in various PDEs, physical meaning

The method of separation of variables produces an undetermined separation constant and a family of solutions indexed by the values of this constant. For instance, in the case of an infinitely long ...
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2answers
132 views

In QM, do we deal with basis or orthonormal sets?

Most textbooks say, that given a (countable) basis ${|\phi_n\rangle}$ of a Hilbert space, that every vector $|\psi\rangle$ of the space can be written as: $$\psi\rangle=\sum_{n=1}^\infty ...
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1answer
230 views

Could two different bases of a Hilbert space have different cardinality? [duplicate]

Here is a quote from http://en.m.wikipedia.org/wiki/Hilbert_space#Hilbert_dimension (accessed: Nov. 22, 2013) : As a consequence of Zorn's lemma, every Hilbert space admits an orthonormal basis; ...
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1answer
170 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}+ ...
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1answer
47 views

Can binary sequences generated from ergodic maps be chaotic?

Chaotic Sequences of IID Binary Random variables with their applications to Communications and related papers by the same author, Tohru Kohda, talk about the statistical properties of binary symbolic ...
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1answer
40 views

A series of bound states covering an interval

Generally, the bound states (normalizable eigenvectors) of a Hamiltonian have discrete eigenvalues. Is it possible for the eigenvalues to cover an interval? Say, $(a,b)$? That is, for each $E \in ...
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0answers
63 views

Books for learning Mathematics in Physics? [duplicate]

Currently I'm doing Advanced Classical Mechanics courses. I'm finding it hard to understand due to the lack of knowledge in linear algebra, multi variable calculus and other chapters. Can anyone ...
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1answer
119 views

If it is given which intervals are spacelike, can be determined which intervals are lightlike?

Provided that the notion of "$\mbox{spacelike}$"-ness (of an interval) is symmetric: $$\text{spacelike}( \, x - y \, ) \Longleftrightarrow \text{spacelike}( \, y - x \, ),$$ then for any set $X$ (of ...