  We introduce a pseudo-mass parameterized Schr\"odinger-like alchemical
equation which contains nuclear charges as variables, treating nuclear charges,
nuclear coordinates and electronic coordinates on the equal footing. The
eigenfunctions of the alchemical equation are the wave functions of nuclear
charges, just like conventional wave functions are of coordinates. A
mathematical definition of alchemical function space is given to hold the
''nuclear charge wave function''. The geometric phase of alchemical dynamics
and alchemical phase space are also derived. For hydrogen-like ion, the
alchemical equation can be simplified into a strong repulsive inverse square
potential equation, which refers to the quantum anomaly and keeps conformal
invariance in non-relativistic quantum mechanics. An extension of the
Hellmann-Feynman theorem, which applies to the non-stationary state in
time-dependent clamped-nuclear-charge alchemical dynamics, is also proved.
