Tagged Questions
3
votes
2answers
59 views
Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$
Quite often (see, for example, this PDF, 50 KB) when discussing the Born-Oppenheimer approximation the following assertion is made: any well-behaved function of two independent variables $f(x,y)$ can ...
4
votes
2answers
144 views
Integer physics
Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.
4
votes
1answer
182 views
How deep can my knowledge of particle physics go without the maths?
Successfully just got my first question answered on here, and now time for the second.
So I recently gained interest in particle physics and was wondering.
By no means do I have the mathematical ...
0
votes
0answers
38 views
How much math do I need to know to learn about quantum mechanics? [duplicate]
I am not good at math, so I needed to know if quantum mechanics involves a lot of math like, astrophysics for example, if it does, is there any book that can teach me this level of math?
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 ...
2
votes
3answers
278 views
Mathematics for Quantum Mechanics [duplicate]
What math should I study if I want to get a basic understanding of quantum mechanics and especially to be able to use the Schrodinger's equation.
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
votes
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 ...
0
votes
2answers
58 views
What is the minimal set of expectation values I need in a statistical model?
At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ ...
7
votes
2answers
698 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 ...
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 ...
2
votes
0answers
159 views
A solvable model for the finite rectangular potential well with a bump in the middle
A well known example in quantum mechanics is that of a finite rectangular potential well with a rectangular bump in the middle. I guess this closely approximates the "umbrella" effect of the $NH_3$ ...
4
votes
3answers
497 views
What is the physical meaning of a “complete” Hilbert space in QM?
What does the word "complete" means from the physical point of view?
I do not understand what it physically means to say that a Hilbert space is a complete vector space.
0
votes
3answers
416 views
Can Planck's constant be derived from Maxwell's equations?
Can mathematics (including statistics, dynamical systems,...) combined with classical electromagnetism (using only the constants appearing in chargefree maxwell equations) be used to derive the planck ...
2
votes
3answers
2k views
What is the math knowledge necessary for starting Quantum Mechanics?
Could someone experienced in the field tell me what the minimal math knowledge one must obtain in order to grasp the introductory Quantum Mechanics book/course?
I do have math knowledge but I must ...
9
votes
2answers
474 views
Transforming a sum into an integral
I posted this in the mathematical forums. Maybe you will help me. I found an hard article http://prola.aps.org/abstract/PR/v105/i3/p776_1 of yang huang and luttinger. The authors begins with the sum: ...
10
votes
7answers
1k views
The philosophy behind the mathematics of quantum mechanics
My field of study is computer science, and I recently had some readings on quantum physics and computation.
This is surely a basic question for the physics researcher, but the answer helps me a lot ...
10
votes
2answers
886 views
Applications of the Spectral Theorem to Quantum Mechanics
I'm currently learning some basic functional analysis. Yesterday I arrived at the spectral theorem of self-adjoint operators. I've heard that this theorem has lots of applications in Quantum ...
