The free Schrodinger equation has localized constant velocity solutions psi(v) of the form psi = f (r - vt) e(i lambda t) with lambda being a constant. These solutions are eigenvectors of a momentum operator (p) over tilde such that (p) over tilde psi(v) = mv psi(v). The wavepacket, while not normalizable, is both localized and in a definite momentum state. The psi(v) are orthogonal in the inner product space hi vertical bar r(2)vertical bar psi >, and the (p) over tilde operator is symmetric therein. We discuss whether these psi(v) can act as basis states rather than the usual plane waves.
展开▼
机译：自由的薛定inger方程具有psi = f（r-vt）e（i lambda t）形式的局部恒速解psi（v），其中lambda是常数。这些解是在代字号上的动量算子（p）的特征向量，使得在代字号psi（v）上的（p）= mv psi（v）。波形包虽然无法归一化，但它既局部化又处于确定的动量状态。 psi（v）在内部乘积空间hi vertical bar r（2）vertical bar psi>中正交，并且代字号（p）在其中对称。我们讨论这些psi（v）是否可以充当基本状态，而不是通常的平面波。
展开▼
