Quantum Chemistry 3.11 - 3-D Particle in a Box

Short lecture on the three-dimensional particle in a box.

The three dimensional particle in a box has a Hamiltonian which can be factored into an independent function of the x, y, and z directions. Thus, we can use separation of variables to express the wave function as a product of three one-dimensional wavefunctions, and solve three individual Schrodinger equations for each dimension. The energy is then a sum of the energy in each dimension. Each dimension has its own quantum number (nx, ny, and nz) all of which can take on any integer value from one to infinity.

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[Creepjacker]

"whenever we have partial differential equations in this course, we have two options: We'll do separation of variables, or we won't solve it" I had a good laugh at that part.

[gillesbaumann]

Your videos are the best man! The overview is simply unique. Keep doing what you're doing cause your doing a great job!

[walacross]

For some stupid reason I couldn’t figure out what I would do if it wasn’t a cubical box due to the equations in my textbook simply writing L^3, but you writing them separately as lx, ly, and lz made it make way more sense, thank you so much :D. Sometimes these simple concepts can be overlooked.

[MeLSL]

You came just in time for my quantum chemistry class this semester. Thank you so much for these helpful videos!!

[PunmasterSTP]

3D particle? More like "Terrific videos, all of em!" Thanks so much for making and sharing them.

[seitdrs]

Hi, what happened to the wave function depending on time? In the separation of variables why isn't there also a time component. Thank your for the comprehensive video guide, it is the best I have found so far.

[dynamicdonut]

does this take into account the boundary conditions psi = 0 and |psi|^2 = 1? Also thank you for this video!

[BlackFiredDragon]

So... what quantum numbers do n_x, n_y, and n_z represent? Like if I'm given the four quantum numbers of a specific particle (n, l, m_l, m_s) in a 3D box, which 3 numbers do I use in finding that particle's energy?

[dps]

6 years later still useful i have an exam tommorow lol

[marybelarenas]

Can you explain what psi* is one more time? I do not understand how/why it is added to the integral function

[aliaabdulaziz]

if the total energy is the sum of energy E_x, E_y and E_z, shouldn't the denominator then be 2m instead of 8m?

[harishkoranga]

How energy get added afte the product of wave?

[karin]

Can someone explain how to draw the specific shape of the particle in the box? For example for 111 the particle would be a sphere?

[mariohernandez]

Is there a way to know when a multidimensional function can be decomposed into a product of unidimensional components?

[josephineamala]

What is lx, ly, lz is.it angular momentum

[Aefryn]

your x and y axis are switched on the graph