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Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

The pressure increases by 1.0 x 104 n/m^2 for every meter of depth beneath the surface of the ocean. at what depth does the volume of a pyrex (bulk modulus 2.6 x 1010n/m^2) glass cube, 9.8 x 10^−2m on an edge at the ocean's surface, decrease by 7.5 x 10−10m^3? explain the formula beyond this point: p=1.0x10^4, b=2.6x10^10, l=9.8x10^−2, delta v=7.5x10^−10. at some point l needs to be cubed. why p is divided by delta v?

The arrival of in the early days of europa’s existence could have formed its ocean. it is likely that the water experienced similar to earth. it is also possible that this water is retained beneath europa’s surface and in its atmosphere due to europa’s . 1.) a. precipitation b. water vapor c. icy debris 2.) a. gravitational compression b. biochemical cycling c. radiogenic heating 3.) a, gravity b. magnetic field c. heat energy for plato