What is Mathematical physics: Definition and 247 Discussions

Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".

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  1. Pushoam

    What is the line integral of a curve?

    Homework Statement Homework EquationsThe Attempt at a Solution Line integral of a curve ## I = \int_{ }^{ } yz dx + \int_{ }^{ } zx dy + \int_{ }^{ } xy dz ## with proper limits. ## I = \int_{\frac { \pi }4}^{ \frac { 3 \pi} 4} abc ( \cos^2 t - \sin^2 t ) dt = -abc ## |I| = abc...
  2. Pushoam

    Solving 2nd order differential equation

    Homework Statement Homework EquationsThe Attempt at a Solution For the homogeneous equation, I have got the the root of the characteristic equation as ## e^{ix}, e^{-ix} ## . So, the corresponding solution is ## B \sin{ x} + A \cos{ x} ## . Then, I took the particular solution as...
  3. Pushoam

    How Does the Function ##\sin(\sinh x)## Behave?

    Homework Statement Homework EquationsThe Attempt at a Solution ## \sinh (x) ## is continuous. ## \sin{( \sinh (x))} ## should have the same amplitude. ...(1) Option (a) and (b) follow this condition. For x = 0, ## \sin ({ \sinh (x)} ) ## = 0. ...(2) Option (a ) follows...
  4. Pushoam

    Determinant of exponential matrix

    Homework Statement Homework EquationsThe Attempt at a Solution [/B] Det( ## e^A ## ) = ## e^{(trace A)} ## ## trace(A) = trace( SAS^{-1}) = 0 ## as trace is similiarity invariant. Det( ## e^A ## ) = 1 The answer is option (a). Is this correct? But in the question, it is not...
  5. fresh_42

    Open problems in mathematical physics

    I came across this beautiful pearl https://arxiv.org/abs/1710.02105 https://arxiv.org/pdf/1710.02105.pdf which I like to bring to notice. Despite of its title it is heavier on theoretical physics than it is on mathematics, so I placed it in this forum. I think it is equally interesting to those...
  6. J

    Applied Zee and Georgi Group Theory books

    Hello. I will be attending a course on Group theory and the book that the professor suggests is Georgi's Lie Algebras in Particle Physics. As I liked Zee's book on General Relativity, I thought that it would be a blast to also use his Group theory textbook for the course. Problem is that I don't...
  7. Q

    Master in theoretical/mathematical physics. Guidance.

    Hello, I was wondering if you could give me some advice on what master’s degree or which specific master courses I should take. I am a physics student and I am going to finish my bachelor in physics next year. I plan to do a master in theoretical physics or in mathematical physics. However I...
  8. Tukhara

    Books for a friend interested in mathematical physics but...?

    Okay, I have a good friend and he is into the idea of becoming a Mathematical Physicist; however, there's several issues at hand. He's in his mid 20's and attends a really cheap community college. Apparently his high school was horrible at teaching students good material; in other words, he...
  9. Eslam100

    What are the topics in theoretical and mathematical physics?

    I'm a rising physics sophomore at a Japanese university. I've studied general physics, linear algebra, and analysis (actually, calculus of single and several variables with emphasis on analysis, everything was proven and the theoretical background was well explained) Other than that, I've...
  10. I

    Physics or mathematics master for mathematical physics?

    Hello! I'm a European physics student with an interest in what I believe to be mathematical physics. I'm torn between going for a master in physics or one in mathematics as more and more it seems to me that the research areas I'm interest are often conducted in the mathematics department...
  11. S

    Mathematical Physics or Standard physics?

    Hello, I'm seriously considering switching degrees to Physics, however I'm not sure whether I should be taking mathematical physics or standard physics (my School has both as separate programs). Which one would you say has better prospects later on? I am planning on getting a Ph.D in this...
  12. M

    I GR for a mathematician and a physicist? What's the difference?

    Have members of the community had the experience of being taught GR both from a mathematical and physics perspective? I am a trained mathematician ( whatever that means - I still struggle with integral equations :) ) but I have always been drawn to applied mathematical physics subjects and much...
  13. AXidenT

    Advice on Graduate Studies in Mathematical Physics

    I recently completed my honours degree in Australia (4-year undergraduate with a year-long thesis and some grad-level subjects such as first courses in algebraic geometry, algebraic topology, GR, QFT and integrable systems) and am struggling to figure out what the best option for graduate study...
  14. smodak

    Explorations in Mathematical Physics

    I just found and bought this book on a whim. I have just glanced through it and have not started reading it seriously yet. I think it is a fascinating book. Have any here read this book? If so, what do you think? https://www.amazon.com/dp/1441921680/?tag=pfamazon01-20 (amazon link)...
  15. Hypercube

    Mathematical physics - writing proofs

    Hi there! So for about a month, I've been self-studying mathematical physics using Mathematical Physics by Hassani. It's a big change for me, after only Stewart calculus, Boyce DE and some linear algebra course, but it's been loads of fun! Now, writing proofs is something fairly new to me, and...
  16. Vitani11

    How would one prepare for mathematical physics?

    I'm taking mathematical physics and mechanics 1 next semester. What do you recommend to prepare? I've taken Calc 1-3, ODE, and (half) a semester of linear algebra. I dropped Linear Algebra midway through this semester because I wasn't prepared to take so many courses while working. Anyway, what...
  17. J

    String Theory and Theoretical vs. Mathematical Physics

    Hello, I have a question about the the difference between mathematical physics and theoretical physics in general and about the difference between the MSc Theoretical and Mathematical Physics courses at Edinburgh in particular. I am planning to apply, however I am not sure which of the two...
  18. L

    From mathematical physics to experimental physics

    Hi, I like mathematical physics and experimental physics, is it possible to change from one to another of these fields after earning PhD from one of them? Thanks
  19. Indiana

    Which is more mathematical?

    Which is more mathematical among The Princeton Companion to Applied Mathematics and Mathematics for Physics by Michael Stone and Paul Goldbart? Both of them are applied mathematics books. What are the main differences between them? Which is more mathematical i.e. mathematically advanced...
  20. B

    Seeking "Reference" Textbooks in Mathematical Physics

    Dear Friends, Could you suggest me some good textbooks in the mathematical physics that I can use for both studying and reference? I am currently reading Landau/Lifshitz' trilogy along with couple other books (Weinberg for gravity, Arnold, etc) in different branches of physics, and I need to...
  21. Liam Lau

    Mathematical Physics or Theoretical Physics

    Hi, I am currently applying to university and am an aspiring Theoretical Physicist. I see many different courses but the two I am not sure on are Mathematical Physics and Theoretical Physics. I was wondering what would give me a better foundation to go on to be a Theoretical Physicist, thank...
  22. Geofleur

    A good way to work through Hassani's Mathematical Physics

    I have learned a lot from reading Sadri Hassani's book "Mathematical Physics", and have also had many frustrations with it. On the one hand, it covers both the classical and the modern methods of mathematical physics, a huge amount of material and at a good level. On the other, it sometimes...
  23. J

    Particle Group Theory book for Undergraduates

    Hello, what are some good books to learn group theory for physicists at an undergraduate level? Is Zee's Group Theory in a Nutshell good? Thanks in advance
  24. P

    Programs What Physics degree would be best for me?

    I like physics because of the formulas, explaining nature in terms of maths (I love math), I love problem solving and it's just so diverse. You learn about subjects from materials to astronomy it's just learning about how stuff works. So topics I like: Kinematics Any mechanics Electricity...
  25. PabloAMC

    Good universities for mathematical physics

    Hi, I would like to know what universities are good at Mathematical Physics for pursuing masters/phds, both in America and Europe. Thanks in advance
  26. J

    Applied Mathematics for physicists books (poll)

    Hello, i want to get a mathematics book for physicists, and i have stumbled across some good books, but as i have not read them yet, i can't really decide which one to buy. So, which one do you prefer and why? Also, do you have any other book to recommend? Thanks!
  27. J

    Guidance regarding Mathematical Physics

    Hello all, I've done an MSc in Physics alongwith a BE in Electronics Engg, graduating in 2014. My scores are quite poor (GPA: 6.23/10), but I am interested in doctoral studies in Mathematical Physics. I wrote exams for PhD admissions here in India for this year but did not fare well enough for...
  28. gravityripple

    Advice on Adult's Path Towards PhD in Mathematical Physics

    Hello, I've read a few of the responses in the guidance section on this site and had some conversations with guidance personnel at my college, but I was hoping to get some other, potentially more objective insights from the group here. I will be 34 this year and am currently a sophomore at a...
  29. A

    Bessel functions and the dirac delta

    Homework Statement Find the scalar product of diracs delta function ##\delta(\bar{x})## and the bessel function ##J_0## in polar coordinates. I need to do this since I want the orthogonal projection of some function onto the Bessel function and this is a key step towards that solution. I only...
  30. A

    Top string theory / mathematical physics programs

    What are some of the top graduate programs in Europe (excluding the UK) on theoretical physics specializing in string theory, fields or mathematical physics?
  31. J

    Mathematical Methods book

    Hello, i am currently enrolled in a Mathematics course which covers these subjects: -Calculus of Variations -Laplace Transform -Fourier Analysis -Special Functions -Integral Equations And as an introduction to the subject it has several things from calculus like maxima/minima of functions of...
  32. G

    Quantum mechanics and mathematical physics textbooks

    Hello!can someone propose a good textbook for quantum mechanics and mathematical physics(including green function)?I would like to buy those books so i want something which is one of the best to have in your libraby!
  33. L

    Who is Tony? A 52-Year-Old Practical Engineer

    Hello I am a 52 year old practical engineer.
  34. J

    Legendre Second Kind: $Q_n(x)$ Functions

    Legendre functions $Q_n(x)$ of the second kind \begin{equation*} Q_n(x)=P_n(x) \int \frac{1}{(1-x^2)\cdot P_n^2(x)}\, \mathrm{d}x \end{equation*} what to do after this step? how can I complete ? I need to reach this formula \begin{equation*} Q_n(x)=\frac{1}{2} P_n(x)\ln\left( \frac{...
  35. B

    Evaluate the partial derivative of a matrix element

    Homework Statement A determinant a is defined in the following manner ar * Ak = Σns=1 ars Aks = δkr a , where a=det(aij), ar , Ak , are rows of the coefficient matrix and cofactor matrix respectively. The second term in the equation is the expansion over the columns of both matrices, δkr is...
  36. Dilatino

    Introduction to Young-tableaux and weight diagrams?

    I am looking for a short pedagogical introduction to Young-tableaux and weight diagrams and the relationship between them, which contains many detailled and worked out examples of how these methods are applied in physics, such as in the context of the standard model and beyond for example. I am...
  37. I

    Physics graduate in need of career advice

    Hello, my name is Israel and I have a B.A. in physics from California State University Stanislaus. I graduated in 2011 in the worst economy ever and in the worst part of the U.S. to be hit by the great recession. I have substitute taught in every subject in K-12, but I am looking to get into the...
  38. K

    Foundations Theoretical Books on Mathematics

    What are some rigorous theoretical books on mathematics for each branch of it? I have devised a fantastic list of my own and would like to hear your sentiments too. Elementary Algebra: Gelfand's Algebra Gelfand's Functions & Graphs Burnside's Theory of Equations Euler's Analysis of the...
  39. H

    Any information about Edinburgh M.Sc Mathematical Physics

    Hey everyone, I just got my admission from the following programs: MSc Mathematical Physics --Edinburgh MSc Theoretical Physics -- Durham MSc Quantum Fields and Fundamental Forces -- IC I have a BSc in Mathematical Science, and I wish to continue a Phd study in particle physics and cosmology...
  40. KimF

    Intro Physics What's a good first physics book for a math major?

    Dear forum members, This is my first post on Physics Forums. I'm very happy to have found this place and to be a member. My question isn't very complicated. I'm a math major with a reasonable grasp of the standard undergraduate analysis curriculum (including differential equations and complex...
  41. J

    What Boundary Conditions Are Needed for Time-Dependent Hermitian Operators?

    Hello, could you please give me an insight on how to get through this proof involving operators? Proof: Given an eigenvalue-eigenvector equation, suppose that the vectorstate depends on an external parameter, e.g. time, and that over it acts an operator that is the fourth derivative w.r.t...
  42. Curieuse

    Prerequisites to Mathematical methods Mary Boas

    Hello! I'm looking to study Mary Boas' Book on mathematical methods and i'd like to know if the prerequisites can be covered in ocw mit courses or any other open courses. Please do suggest if any. Also are there any parallels that can be drawn with the ocw mit courses for the various topics...
  43. R

    Mathematical Physics graduate programs?

    I have a master's in physics. I'm looking at PhD programs, but I really don't want to take the same courses over and take comprehensive exams (or the damn GRE). I managed to squeeze in a few math classes before I finished. I would like to do research in physics, but from a more math-heavy...
  44. terra

    Volume elements of phase space

    First, two definitions: let ## \varrho (M)## be the probability density of macro states ##M ## (which correspond to a subgroup of the phase space) and ## \mathrm{d} \Gamma ## be the volume element of a phase space. In my lecture notes, the derivation for continuity equation of probability...
  45. N

    Mathematical Physics vs Theoretical Physics

    Hello PF, pardon me if this isn't the wrong place but I just had a quick question. So I have always wanted to do Theoretical Physics (particular interests are Quantum Gravity, Cosmology, QFT and Quantum Optics, but those are subject to change), but recently I have started to look into...
  46. D

    To be or not to be a mathematician or a physicist?

    Hello! I'm in my final high school year (Bachillerato, as we call it in Spain) and I have to choose between getting a degree in physics or mathematics. Frankly, my uni's approach to physics is far more experimental than theoretical. I do not like that (lol). I love mathematics, and just reading...
  47. Z

    Geometric measure of entanglement for fermions or bosons?

    For a system consisting of multiple components, say, a spin chain consisting ofN≥3spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner product between the wave function and a simple tensor product wave function. But it seems that none used this...
  48. Vinay080

    Why can't a particle ever reach a non-terminating decimal form radian value?

    Consider a particle P moving in a circle of radius r as shown in the figure. Premise 1: Position of the particle can be described by the angle θ. Premise 2: Particle reaches the position with an angle θ if it has covered the angle lesser than θ. Premise 3: Particle can never reach...
  49. M

    Where does Mathematical Physics reside?

    Where exactly does this area of study reside? Is it within the math department or the physics department? More specifically, do you need to get accepted into a math or physics graduate program? The undergraduate mathematical physics program here is listed under both the math and physics degrees...
  50. Quantum_Gorilla

    Studying Best books for learning Plasma Physics?

    Hi there, So I have two questions really. My first question is, I'm having a bit of trouble finding which books I should get to teach myself plasma physics. My school doesn't offer a course on the subject, sadly, so I asked my professors, who do nuclear research, and they didn't know which...
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