Quantum Monte Carlo ingredients, the local energy

Define a new quantity

$$E_L(\boldsymbol{R},\boldsymbol{\alpha})=\frac{1}{\psi_T(\boldsymbol{R},\boldsymbol{\alpha})}H\psi_T(\boldsymbol{R},\boldsymbol{\alpha}), \tag{1}$$

called the local energy, which, together with our trial PDF yields

$$E[H(\boldsymbol{\alpha})]=\int P(\boldsymbol{R})E_L(\boldsymbol{R}) d\boldsymbol{R}\approx \frac{1}{N}\sum_{i=1}^N E_L(\boldsymbol{R_i},\boldsymbol{\alpha}) \tag{2}$$

with $N$ being the number of Monte Carlo samples.

• «
• 1
• ...
• 20
• 21
• 22
• 23
• 24
• 25
• 26
• 27
• 28
• 29
• 30
• 31
• 32
• 33
• 34
• 35
• 36
• 37
• »