How does de Broglie postulate enter into the Schroedinger theory?

[Mitadru Banik]

How does de Broglie postulate enter into the Schroedinger theory?

 

[hilbert2]

In position-representation (Schrödinger) quantum mechanics, the momentum operator is ${\bf p}=-i \hbar \frac{\partial}{\partial x}$ and a plane wave wavefunction of wavelength $\lambda$ is $\psi (x) = e^{2 \pi i x / \lambda}$. If you operate on the plane wave with the momentum operator, you get ${\bf p} e^{2 \pi i x / \lambda}=\frac{2 \pi \hbar}{\lambda}e^{2 \pi i x / \lambda}$, i.e. the plane wave is a momentum eigenstate with momentum $p = \frac{2 \pi \hbar}{\lambda} = \frac{h}{\lambda}$. This relation between momentum and wavelength is exactly the De Broglie postulate.

So, we see here that the DB postulate is "built-in" in the Schrödinger wave mechanics.

 

[Mitadru Banik]

What happen if the function is an harmonic oscillator function?

 

[hilbert2]

The solutions of harmonic oscillator Schrödinger equation are not momentum eigenstates. The fact that De Broglie momentum-wavelength relation is reproduced in Schrödinger QM must be demonstrated with the free-particle system (in which the solutions of SE are plane waves with well defined momentum and wavelength).

 

[Mitadru Banik]

can you suggest me a good textbook for quantum mech which will help me to clear any interview in quantum mech.. please its urgent..i have an interview in between 2 weeks...

 

[Vic Sandler]

Principles of Quantum Mechanics by R. Shankar is one of many good quantum mechanics textbooks. But before you run out and buy it or any other, you should let us know what the interview is for and what your mathematics and physics background is. Is the interview for a job, or for school placement or for what? Have you had calculus, differential equations, linear algebra, and/or a basic physics survey course?

 

[Bill_K]

can you suggest me a good textbook for quantum mech which will help me to clear any interview in quantum mech.. please its urgent..i have an interview in between 2 weeks...

You aren't going to be able to learn Quantum Mechanics from scratch in two weeks, especially if you don't already have a book on the subject. And nothing turns an interviewer off faster than the sense that you're trying to bluff him out. My advice is to be honest and admit that you're not very familiar with it.

 

[Vic Sandler]

I disagree. You will benefit more from trying and failing than you will from not trying. You can't learn all of QM in two weeks, but you may learn enough to pass the interview.

 

[Bill_K]

I disagree. You will benefit more from trying and failing than you will from not trying. You can't learn all of QM in two weeks, but you may learn enough to pass the interview.

I guess my comment comes from experience dealing with TA's who said they knew Quantum Mechanics and didn't.

 

[Mitadru Banik]

I have already read Resnick and Eisberg but still there are many confusions about the subject which is not good for my interview. Actually the interview is for my MSc admission. So i need a easy book which can remove my most of the confusions about the subject.

 

[gadong]

What happen if the function is an harmonic oscillator function?

The de Broglie model describes free particles, which have constant momentum and hence a well-defined and constant wavelength.

For particles that move through regions of changing potential, the wavelength changes from point to point. If you want to pursue this analogy, think of light moving through a region of changing refractive index: the wavelength changes from point to point. To describe light "waves" mathematically in this situation you would need to consider contributions from more than one wavelength, i.e. by using a sum of harmonic terms, otherwise known as a Fourier series or integral.

The wave functions that arise in the Schroedinger equation can similarly be thought of as Fourier series or integrals of harmonic functions that conform to certain boundary conditions.

...Incidentally, looked at in this way, the momentum operator mentioned above by Hilbert2 appears naturally as a (well-known) mathematical property of Fourier transforms.