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Math Physics


  • 1:19:24 Mathematical Physics 01 - Carl Bender

    Mathematical Physics 01 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 1Perturbation series. Brief introduction to asymptotics.

  • 1:23:51 Mathematical Physics 02 - Carl Bender

    Mathematical Physics 02 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 2The Schroedinger equation. Riccati equation. Initial value problem. Perturbation series approach to solving the Schroedinger equation. The eigenvalue problem.

  • 1:26:49 Mathematical Physics 03 - Carl Bender

    Mathematical Physics 03 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 3Putting a perturbative parameter in the exponent. Thomas-Fermi equation. KdV equation. Eigenvalue problem - analytic structure of the energy function. The square root function. Branch cuts. Shank

  • 1:24:47 Mathematical Physics 04 - Carl Bender

    Mathematical Physics 04 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 4Acceleration of convergence. Shanks transform. Richardson extrapolation. Summing a divergent series. Euler summation. Borel summation. Generic summation machines.

  • 1:23:38 Mathematical Physics 05 - Carl Bender

    Mathematical Physics 05 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 5Summation of divergent series continued. Analytic continuation of zeta and gamma functions. The anharmonic oscillator.

  • 1:25:57 Mathematical Physics 06 - Carl Bender

    Mathematical Physics 06 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 6Continued fractions. Pade sequence. Stieltjes series.

  • 1:15:56 Mathematical Physics 07 - Carl Bender

    Mathematical Physics 07 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 7Pade technique for summing a series. Asymptotic series. Fuchs' theorem. Frobenius series.

  • 1:23:59 Mathematical Physics 08 - Carl Bender

    Mathematical Physics 08 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 8Local analysis. Asymtotic series solution to differential equations continued. WKB approximation.

  • 1:30:52 Mathematical Physics 09 - Carl Bender

    Mathematical Physics 09 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 9Asymptotic series solution to differential equations continued

  • 1:22:42 Mathematical Physics 10 - Carl Bender

    Mathematical Physics 10 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 10Asymptotic solutions to the inhomogeneous Airy equation. The rigourous theory of asymptotics. Stieltjes functions. The four properties of Stieltjes functions. Herglotz property

  • 1:30:43 Mathematical Physics 11 - Carl Bender

    Mathematical Physics 11 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 11Proof of Herglotz property of Stieltjes functions. Stieltjes functions and the convergence of Pade sequences. The moment problem. Carleman condition.

  • 1:25:54 Mathematical Physics 12 - Carl Bender

    Mathematical Physics 12 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 12Asymptotic distribution of the number of Feynman diagrams in phi^4 theory. Comparison with phi^6 and phi^8 theories. Sketch of the precise asymptotic expression for the coefficient of the pertur

  • 1:26:09 Mathematical Physics 13 - Carl Bender

    Mathematical Physics 13 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 13Accuracy of WKB. Solution to the Sturm-Liouville problem using WKB. Turning points.

  • 1:30:15 Mathematical Physics 14 - Carl Bender

    Mathematical Physics 14 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 14

  • 1:31:30 Mathematical Physics 15 - Carl Bender

    Mathematical Physics 15 - Carl Bender

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    PSI Lectures 2011/12Mathematical PhysicsCarl BenderLecture 15

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