Sains Ma1aysiana 25(1): 111-125 (1996)                                                                          Sains Matematik/

                                                                                                                                     Mathematical Sciences

 

Penyelesaian Kamiran Nyata Berbentuk Kamiran

Feynman bagi Persamaan Resapan Teritlak

Berpotensi Ayunan Harmonik

(Exact real integral solution in the Feynmann integral form for

a generalized diffusion equation with an harmonic potential)

 

 

Shaharir bin Mohamad Zain & Zainal bin Abdul Aziz

Jabatan Matematik

Fakulti Sains Matematik

Universiti Kebangsaan Malaysia

43600 UKM Bangi Selangor D.E. Malaysia

 

 

ABSTRAK

 

Penyelesaian tepat berkamiran nyata diperoleh dalam bentuk yang serupa dengan penyelesaian kamiran Feynman yang sedia ada, bagi persamaan resapan teritlak berpotensi pengayun harmonik

 

ABSTRACT

For the generalised diffusion equation with the potential of an harmonic ascillator, we obtain the exact real integral solution in a form similar to the existing Feynman integral solution.

 

 

RUJUKAN/REFERENCES

 

Albeverioo, S. A. & Hoegh-Krohn, R. J. 1976. Mathematical theory of Feynman pth integral. Lecture Notes in Math. 523 Berlin: Springer-Verlag.

Blanchard, Ph., Combe, Ph. & Zheng, W. 1987. Mathematical and physical aspects of stochastic mechanics. Lecture Notes in Phys. 281. Berlin: Springer-Verlag. Butkov, E. 1968. Mathematical Physics. Reading, Mass: Addison-Wesley.

Cameron, R. H. 1960. A family of integrals serving to connect the Weiner and Feynman integrals. J. Maths. phys. 39: 126-140.

Carreau, M., Farhi, E., Gutmann, S. & Mende, P. F. 1990. The functional integral for quantum systems with hamiltonians unbounded from below, Annals of Physics 204: 186-207.

Carrier, G. F., Krook, M. & Pearson, C. E. 1966. Functions of a complex variable.

New York: McGraw Hill DeWitt-Morette, C. & Elworthy, K. D. 1981. New stochastic methods in physics. Phys. Rep. 77. no 3.

Elworthy, K. D. 1982. Stochastic Differential Equations on manifolds. LMS series 70, Cambridge: Cambridge Univ. Press.

Feynman, R. P. 1984. Space-time appoach to non-relativistic quantum mechanics. Rev. Mod. Phys. 20: 367-387.

Hida, T. 1980. Brownian Motion. New York: Springer-Varlag.

Ito, K. 1951. On stochastic differential equation. Mem Amer. Math Soc. No.4.

Ito, K. & Mckean, JR H. P. 1974. Diffusion processes and their sample paths. Berlin: Springer- Verlag.

Kac, M. 1951. On some connections between probability theory and differential and integral equations. Proc. Second Berkeley Symp. on Math. Statist. and Probabil­ity, 189-215.

Kallianpur, G., Kannan, D. & Karandikar, R. L. 1985. Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula. Ann. Inst. Henri Poincare'. 21: 323-361. 

Khandekar, N. C., Lawande, S.V. & Bhagwat, K. V. 1993. Path-integral methods and their applications. Singapore: World Scientific.

Landau, L. D. & Lifshitz, E. M. 1977. Quantum Mechanics (non - relativistic theory) Ed. ke 3. London: Pegamon Press.

Lighthill, M. J. 1964. Introduction to Fourier analysis and generalised functions.Cambridge: Cambridge univ. press.

Nagasawa, M. 1993. Schroedinger equations and diffusion theory. Basel: Birkhauser Verlag;

Nelson, E. 1964, Feynman integrals and the Schroedinger equation. J. Math.Phys. 5: 332-343.

Roach, G. F. 1982. Green's Functions. Ed. ke-2 Cambridge: Cambridge Univ. Press. Schulman, L. S. 1981. Techniques and applications of path integration. New York: John Wiley.

Shaharir, b. M. Z. 1986. Teori penjelmaan Fourier dan kegunaannnya. Dewan Bahasa dan Pustaka, Kuala Lumpur.

Shaharir, b. M. Z. 1986. New framework for the Feynman integral. Int. Jour. Theor. Phys. 10: 1075-1094.

Shaharir, b. M. Z. 1987. On complex normal distribution. Sains Malaysiana 16. 397-408.

Shaharir b. M. Z. 1994. Penyatuan proses resapan kalsik dengan persamaan Schroedinger bagi potensi afin. Pembentangan di Seminar Jabatan Matematik, Universiti Malaya, 7 Sept. 1994. (pracetak)

Shaharir, b. M. Z. & Zainal, b. A. A. 1994a. Catatan mengenai penyelesaian kamiran nyata yang tepat bagi persamaan resapan linear teritlak. Kertas kerja Simposium Kebangsaan Sains Matematik ke IV, 3-5 Mei 1994, Universiti Malaya, Kuala Lumpur.

Shaharir, b. M. Z. & Zainal b. A. A. 1994b. Perihal penyelesaian kamiran nyata yang tepat bagi persamaan resapan berpotensi linear. Kertas kerja Seminar Siswazah FSMK, 6 Sept. 1994, UKM Bangi.    

Shaharir, b. M. Z. & Zainal, b. A. A. 1994C. Kamiran nyata bersebutan lintasan kalasik bagi model resapan teritlak yang berpotensi kuadratik dlaam ruang unimatra. (dalam persediaan).

Simon, B. 1979. Functional integration and Quantum Physics. New York: Academic press.

Wiegel, F. W. 1986. Introduction to path-integral methods in physics and polymer physics. Singapore: World Scientific.

 

 

previous