A Universally Valid Uncertainty Relation Revisited

A universally valid uncertainty relation proposed by Ozawa is re-investigated under for the generalized equation of motion with some boundary condition. Necessary conditions for violation (lessening) of the Heisenberg-type uncertainty relation is discussed in detail. An experimental test of lessening of the generalized uncertainty relation due to the boundary condition is shown by re-analyzing the data measuring electron densities of hydrogen molecule encapsulated in a cage of fullerene C60.