Supersymmetry in the Half-Oscillator - Revisited
  Following a recent study by Das and Pernice [Nucl. Phys. B561, (1999) 357], we have carefully analyzed the half-harmonic oscillator. In contrast to their observations, our analysis reveals that the spectrum does not allow for a zero energy ground state and hence the supersymmetry is broken when the domain is restricted to the positive half of the real axis. 
Asim Gangopadhyaya and Jeffry V. Mallow