Sains Malaysiana 32: 93-110 (2003)                                                              Sains Fizis dan Gunaan /

Physical & Applied Science

Zarah Schroedinger Bebas atas Garis sebagai suatu Resapan

(Free Schroedinger particle above real line as a diffusion)

Shaharir Mohamad Zain & Nik Rusdi Yaacob

Pusat Pengajian Sains Matematik

Fakulti Sains dan Teknologi Universiti

Kebangsaan Malaysia 43600 UKM Bangi

Selangor D.E., Malaysia

ABSTRAK

Modulus kuasa dua fungsi gelombang zarah bebas yang bersyarat awal fungsi taburan normal ditunjukkan bertaburan normal dengan min yang sama tetapi bervarians yang berbeza. Oleh itu modulus fungsi gelombang itu dan kuasa duanya memenuhi persamaan resapan yang berpekali resapan  berpekali hanyutan   dengan F ialah fasa fungsi gelombang itu tetapi masing-masingnya bersumberkan potensi yang berbeza dan bergantung pada terbitan pertama fasa fungsi gelombang itu. Untuk syarat awal sebarang fungsi yang kuasa duanya terkamirkan, modulus dan modulus kuasa dua fungsi gelombang yang sepadannya dibuktikan memenuhi persamaan resapan yang serupa dengan fasa yang sepadannya. Pengecaman proses resapan secara terus ini dapat menjadi satu lagi alternatif terhadap pemahaman tabii fungsi gelombang dalam persamaan Schroedinger itu di samping kaedah-kaedah yang lain yang disorot di sini.

ABSTRACT

The square of the modulus of the wave function for a free particle with a normal distribution as its initial condition is shown to be a normal distribu­tion with the same mean but a different variance. Further, it is shown that the modulus of the wave function and its square satisfy a diffusion equation with a diffusion coefficient   and a drift coefficient     where F is the phase of the wave function, but each with a different potential source which depends on the first derivative of the phase of the wave function. For an arbitrary square integrable function as its initial condition, it is shown that the modulus of the wave function and its square also satisfy similar diffusion equations with the corresponding phase of the wave function. The identification of the diffusion process directly in this way provides another alternative method in understanding the nature of the wave function in the Schroedinger equation beside those other methods which are reviewed here.

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