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ito_integral [2016/07/06 13:00] nikolaj |
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| I.e. the Itō integral is defined with most left of the grid cells as in the explicit Euler-method numerical approximation scheme. The implicit Euler-method simply corresponds to a different notion of integral here and would give a different result. | I.e. the Itō integral is defined with most left of the grid cells as in the explicit Euler-method numerical approximation scheme. The implicit Euler-method simply corresponds to a different notion of integral here and would give a different result. | ||
| - | In quantum mechanics, the difference of the product above | + | In quantum mechanics, the difference of the products |
| $[x,p]_{\Delta t}:=x(t+\delta^2{\Delta t})\,p_{\Delta t}(t)-x(t)\,p_{\Delta t}(t)$ | $[x,p]_{\Delta t}:=x(t+\delta^2{\Delta t})\,p_{\Delta t}(t)-x(t)\,p_{\Delta t}(t)$ | ||
| - | is $m\,\kappa^2=m\frac{i\hbar}{2m}=\frac{i\hbar}{2}$. | + | is |
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| + | $m\,\kappa^2=m\frac{i\hbar}{2m}=\frac{i\hbar}{2}$. | ||
| == Fractional quantum mechanics == | == Fractional quantum mechanics == | ||
