According to De Broglie's eqn by calculating momentum of electron in 1st orbit of hydrogen, the wavelength is itself the diameter of the atom, so what does it tell abt the wave function? In general what is the relationship between De Broglie's eqn and wave function? In case my question is wrong , then please help me correct my thinking. I am a 11th std student.
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1$\begingroup$ Have you read the Wikipedia article on matter waves? $\endgroup$– ACuriousMind ♦Commented Jun 7, 2015 at 19:16
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1$\begingroup$ De Broglie's waves were among the first serious attempts to understand quantum mechanics and the idea was just a few years later replaced by proper quantum theory. It has a place in science history, but one should't take it too seriously because it detracts too much from what we know for good about the microscopic world. Honestly, in my personal opinion it shouldn't be taught anymore because once it gets stuck in ones mind its hard to get rid off in favor of the real stuff. $\endgroup$– CuriousOneCommented Jun 8, 2015 at 0:26
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The wave function in an atom can be written as a sum of wave functions of the form
$\Psi_{\vec{k}}(\vec{r})=e^{i\vec{k}\cdot\vec{r}}$
In using deBroglie's equation $p=\hbar k$ to estimate the momentum of an electron in a hydrogen atom, you are assuming that the dominant wave function $\Psi_{\vec{k_0}}$ in the sum has a wave vector $\vec{k_0}$ such that
$$k_0=\frac{2\pi}{\lambda_0}$$
where $\lambda_0$ is the diameter of the atom. In this way, you can see how using deBroglie's equation to estimate the average momentum of an electron in an atom is actually a crude approximation that leaves out all the terms in the wave function with momenta different from $\hbar k_0$.
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$\begingroup$ Thanks i can see some correlation between de broglie's eqn and wave function. Will need some time to understand it. Anyways thanks. $\endgroup$ Commented Jun 10, 2015 at 17:14