Tagged Questions
2
votes
1answer
69 views
Limit of an n-ary product
Since a definite integral is defined as
$$\lim_{n\to\infty} \sum_{i=0}^n f(x_i^*)\,\Delta x = \int_a^b f(x)\,dx$$
and the integral is much easier to calcluate than a sum, if we change the sum to a ...
4
votes
1answer
162 views
Is there a “continuous product”?
Is there a "continuous product" which is the limit of the discrete product $\Pi$, just like the integral $\int$ is the limit of summation $\sum$.
Thanks!
3
votes
1answer
116 views
Dyson series and T product (II)
After reading the previous posts related to the Dyson series, I have decided to open a new thread because there is something that I am still not understanding. It concerns the expression:
$$
...
4
votes
1answer
285 views
Dyson series and T product
One of the most important tool in quantum mechanics is the Dyson series because it is the basis of the perturbative theory. There is a step in the derivation that I can't understand.
$\{H(t_i)\}$ are ...
20
votes
4answers
818 views
What is to geometric mean as integration is to arithmetic mean?
The arithmetic mean of $y_i ... y_n$ is: $$\frac{1}{n}\sum_{i=1}^n~y_i $$
For a smooth function $f(x)$, we can find the arithmetic mean of $f(x)$ from $x_0$ to $x_1$ by taking $n$ samples and using ...
