New developments since January 1995 are recorded in the updates document. Please contact David Ceperley if you discover other errors.

• Equation 2.10 is not an exact operator identity except if T and V commute with their commutator [T,V]. In general one has to use the Bakker-Campbell-Hausdorff formula to expand exp(-t H) into the product e(-tT)e(-tV). The justification of the Trotter formula (2.12) is not as straightforward but can be done. Thanks to F. Laloe.

   

• Section III.H Table I pg 306: In the table caption, "density" should be "molar volume". The label of the last exchange in the table is incorrect--instead of (1^6;123^2;417) it should read (1^6; (523)^2; 417).

   

   

• Section V.A: Path Sampling Methods: Molecular Dynamics. It was shown in Martyna, G.J., Klein, M.L., Tuckerman, M., J. Chem. Phys. 97, 2635 (1992) that standard Nose-Hoover thermostats are not enough to mix the canonical PIMD trajectories for harmonic oscillators, and that what one has to do is to apply chains of Nose-Hoover thermostats. In this case, however, even the pathological harmonic oscillator is forced to be ergodic. Thanks to D. Marx.

   

• pg. 326, below Eq. (523) the expression S\chi +R_m should be S\chi+{\barR}_m. Thanks to Denis Baiko.

   

• Section V.G (pg. 329) The Levy construction. The sentence following Eq. 5.35 should end with sqrt (lambda|t2-t1|/2 ). (note extra factor of 2). Thanks to R. Fantoni.

   

• Eq. (6.8) has the wrong sign for the kinetic energy.

   

• The RHS of Eq. (6.11) should contain E_T not E_D.

   

• In Eq. (6.13) the superscript of the first term on the RHS should be Uⁱ⁺¹ NOT (i-1). Thanks to R. Fantoni.

   

• The potential term in (6.17) has the wrong sign. It should be -2R_i DEL U. Thanks to R. Fantoni.
• Figure 54 and Section VII.B comparing PIMC resul was out of date. Optimized shadow wave functions have significantly lower energies. See MacFarland et al., Phys. Rev. 50, 13577 (1994) and the revised postscript figure 54 . All data are at the experimental equilibrium density of liquid 4He. Thanks to L. Reatto.

   

• Section VII.D: Comparison with other Quantum Monte Carlo methods: Effective-potential Monte Carlo. I should have also referred to the earlier work of V. Tognetti and R. Giachetti Phys. Rev. Lett. 912 (1985) and Phys. Rev B33,7647 (1986), J.Magn.Mat. 54-57, 861 (1986).
• The up-to-date review on the application of Maximum entropy methods to imaginary time correlation functions by Jarrell and Gubernatis has appeared: Physics Reports, 269, 135 (1996). (it was a preprint before)

   

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