  A magnetic field, through its vector potential, usually causes measurable
changes in the electron wave function only in the direction transverse to the
field. Here we demonstrate experimentally and theoretically that in carbon
nanotube quantum dots, combining cylindrical topology and bipartite hexagonal
lattice, a magnetic field along the nanotube axis impacts also the longitudinal
profile of the electronic states. With the high (up to 17T) magnetic fields in
our experiment the wave functions can be tuned all the way from "half-wave
resonator" shape, with nodes at both ends, to "quarter-wave resonator" shape,
with an antinode at one end. This in turn causes a distinct dependence of the
conductance on the magnetic field. Our results demonstrate a new strategy for
the control of wave functions using magnetic fields in quantum systems with
nontrivial lattice and topology.
