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projects_divergentphysics [2020/04/10 13:06] trinh created |
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| V(x) = \frac{1}{2} x^2. | V(x) = \frac{1}{2} x^2. | ||
| $$ | $$ | ||
| - | You learn that the permissible energies take discrete values like $E_n = n + 1/2$. In an effort to understand how this can be generalised, | + | You learn that the permissible energies take discrete values like $E_n = (n + 1/2)$. In an effort to understand how this can be generalised, |
| $$ | $$ | ||
| V(x) = \frac{1}{2} x^2 + \lambda x^4. | V(x) = \frac{1}{2} x^2 + \lambda x^4. | ||
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| E_n = \left(n + \frac{1}{2}\right) + \lambda E_{n1} + \lambda^2 E_{n2} + \ldots = \sum_{j=0}^\infty \lambda^n E_{nj}. | E_n = \left(n + \frac{1}{2}\right) + \lambda E_{n1} + \lambda^2 E_{n2} + \ldots = \sum_{j=0}^\infty \lambda^n E_{nj}. | ||
| $$ | $$ | ||
| - | But doing so, you quickly realise that the series is divergent. How do you assign meaning to a divergent series? Perhaps put more sensationally: | + | But doing so, you quickly realise that the series is divergent |
| - | + | ||
| - | This problem lies at the heart of a lot of the puzzling issues about quantum theories---mainly that many of the quantities that you try to write down are divergent, and it is not clear how to extract meaning from them. | + | |
| This project will be about learning about some of these techniques for studying divergent series. | This project will be about learning about some of these techniques for studying divergent series. | ||