δ函数及在量子力学中的应用

δ Function and its Physical Applications

δ函数不同于一般数学函数,阐述了δ函数的引入及主要性质,利用δ函数的定义处理了量子力学中连续谱本征函数的归一化和本征值取连续谱的算符在自身表象中的本征函数问题,应用δ函数作为广义函数可看成函数序列的极限、原函数为阶跃函数及其傅里叶积分求解了δ势、量子跃迁问题,从而揭示了δ函数在解决量子力学问题的优越性.

δ Function is different from general mathematical functions. The introduction of δ function and its main properties is expounded. Several theoretical and practical problems in quantum mechanics are discussed. The normalization of continuous spectrum of eigenfunction and the eigenfunction of the operator with continuous spectrum in itself representation is dealt with through the definition of δ function. δ potential and quantum transition is solved by seeing δ function as the limit of the sequence of functions and its Fourier integral. Finally,the superiority of the function in solving the problem of quantum mechanics is revealed.