Physical significance of minimum uncertainty states of an angular momentum system
H. Bacry · Physical Review A · 1978
The minimization of the uncertainty relation $2\ensuremath{\Delta}x\ensuremath{\Delta}p\ensuremath{\ge}\ensuremath{\hbar}$ characterizes the coherent states. The spincoherent states of Radcliffe minimize the uncertainty relation $2\ensuremath{\Delta}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{u}})\ensuremath{\Delta}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}})\ensuremath{\ge}|〈\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{w}}〉|$ (where $\stackrel{\ensuremath{\rightarrow}}{\mathrm{u}}$, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{w}}$ form an arbitrary orthonormal basis), but this property does not characterize them. Here, we analyze that situation and suggest an alternative to restore the parallelism.