论文标题
轨道角动量操作员特征值问题的新颖前景
Novel Outlook on the Eigenvalue Problem for the Orbital Angular Momentum Operator
论文作者
论文摘要
基于复杂数字的功率的新颖处方，提出了角动量第三个成分的操作员特征功能的新表达式。这些函数是可正常的，单个值，并且在2π下在2π下不变，而不是必需的整数m-角动量第三个成分的操作员的特征值。对于任何实际m，这些函数形成了正统集合，因此它们可以用作量子机械征函数。报道了平方的角动量操作员的算子的特征值和特征值，该算子是针对平方根的两个不同处方得出的。角动量操作员平方的操作员的正常本征函数以超几何函数的形式呈现，承认整数以及非整体特征值。结果表明，纯整数频谱不是最通用的解决方案，而只是特定选择legendre的伪像，作为对角动量操作员平方的操作员特征值问题的线性独立解决方案。
Based on the novel prescription for the power of a complex number, a new expression for the eigenfunction of the operator of the third component of the angular momentum is presented. These functions are normalizable, single valued and are invariant under the rotations at 2πfor any, not necessary integer m - the eigenvalue of the operator of the third component of the angular momentum. For any real m these functions form an orthonormal set, therefore they may serve as a quantum mechanical eigenfunctions. The eigenfunctions and eigenvalues of the operator of the angular momentum operator squared, derived for the two different prescriptions for the square root are reported. The normalizable eigenfunctions of the operator of the angular momentum operator squared are presented in terms of hypergeometric functions, admitting integer as well as non-integer eigenvalues. It is shown that the purely integer spectrum is not the most general solution but is just the artifact of a particular choice of the Legendre functions as the pair of linearly independent solutions of the eigenvalue problem for the operator of the angular momentum operator squared.
