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quantum_integer [2014/12/09 22:25] nikolaj |
quantum_integer [2014/12/10 12:01] nikolaj |
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| In fact this doesn't require $n$ to be an integer. | In fact this doesn't require $n$ to be an integer. | ||
| - | The case $f=0$ is often considered, and also $[n]_{q^2}$ together with $f=n-1$, where the numbers are of the form $n+\mathcal{O}\left((q-1)^2\right)$. In the imaginary direction, $q\propto\mathrm{e}^{i\varphi}$, this corresponds to $\lim_{\varphi\to 0}\frac{\sin(n\varphi)}{\sin(\phi)}=n$. | + | Quantum aspect: The case $f=0$ is often considered, and also $[n]_{q^2}$ together with $f=n-1$, where the numbers are of the form $n+\mathcal{O}\left((q-1)^2\right)$. In the imaginary direction, $q\propto\mathrm{e}^{i\varphi}$, this corresponds to $\lim_{\varphi\to 0}\frac{\sin(n\varphi)}{\sin(\phi)}=n$. |
| - | + | With $q=r\mathrm{e}^{i\varphi}$, along the positive real axis number $[n]_q$ is a valley with bottom at $q=1$, where $[n]_{1}=n$, and along $\varphi$ you have harmonic oscillations with period depending on $n$. | |
| - | Then, with $q=r\mathrm{e}^{i\varphi}$, along the positive real axis number $[n]_q$ is a valley with bottom at $q=1$, where $[n]_{1}=n$, and along $\varphi$ you have harmonic oscillations with period depending on $n$. | + | |
| >I might change the exponent in $-f(n)/2$ to something else later | >I might change the exponent in $-f(n)/2$ to something else later | ||
