Calculate a three-dimensional infinite square well potential of dimensions a,b and c in the x,y and z dimensions, respectively. (a) Write time-independent 3D Schröedinger equation in Cartesian coordinates and the corresponding general solution. (b) How many and which are the quantum numbers (nx, ny, nz) degenerate states will exist for the fourth energy state (E4)?
Calculate a three-dimensional infinite square well potential of dimensions a,b and c in the x,y and z dimensions, respectively. (a) Write time-independent 3D Schröedinger equation in Cartesian coordinates and the corresponding general solution. (b) How many and which are the quantum numbers (nx, ny, nz) degenerate states will exist for the fourth energy state (E4)?
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I posted this question and got like a photo from a solution book . Not taking anything away but certain terms are not even being used in this stage of Radiation physics like the Hamiltonian operator. (
Transcribed Image Text:Calculate a three-dimensional infinite square well potential of dimensions a,b and c in the
x,y and z dimensions, respectively.
(a) Write time-independent 3D Schröedinger equation in Cartesian coordinates and the
corresponding general solution.
(b) How many and which are the quantum numbers (nx, ny, nz) degenerate states will exist
for the fourth energy state (E4)?
Transcribed Image Text:Y (4) = B sin(they y), Tey
Ta 9 (x,g,z) = X Y(9) Z (a)
Caleulate Fortih
3.5
text BoK
%3D
7°4+°pcx.yy,4) =0
%3D
The genad solution for each Coordinete is:
X (x) = A silterx)
fex=
%3D
%3D
a
Y(4) = B si(thg y), Pen = My TT
%3D
Z(2)
Z (2) = C ain (ke z), k, = MaT
%3D
%3D
2.
%3D
nz
C2
(b) Assumg a=6%3Dc (a2 in de text book)
state
the fourth eury
coreeponds to
= 11
%3D
and (Mx, My, Mg) =(1.1, 3))
(1,3,1)
(3, 1,1)
Gud
ie three
degenerate
states.
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