Wolfram Cloud Document

1.PozodePotencialInfinitoen1D

Antesdeabordarlavisualizaciónen3D,confirmemosqueelcódigopara1Dfuncionacorrectamente.

a.FuncionesdeOndaEstacionariasyDensidadesdeProbabilidad

In[]:=

(*Parámetrosdelpozo*)L=1;(*Longituddelpozo*)nMax=4;(*Númeromáximodeestadosavisualizar*)m=1;(*Masadelapartícula*)ħ=1;(*ConstantedePlanckreducida*)(*Definirlafuncióndeondaestacionaria*)psi[n_,x_]:=Sqrt[2/L]Sin[nPix/L](*Definirladensidaddeprobabilidad*)probDensity[n_,x_]:=Abs[psi[n,x]]^2(*Graficarlasfuncionesdeonda*)Plot[Evaluate[Table[psi[n,x],{n,1,nMax}]],{x,0,L},PlotLegends"Expressions",PlotRangeAll,AxesLabel{"x","ψ_n(x)"},PlotLabel"Funciones de Onda Estacionarias en 1D",FillingAxis](*Graficarlasdensidadesdeprobabilidad*)Plot[Evaluate[Table[probDensity[n,x],{n,1,nMax}]],{x,0,L},PlotLegends"Expressions",PlotRangeAll,AxesLabel{"x","|ψ_n(x)|^2"},PlotLabel"Densidades de Probabilidad en 1D",FillingAxis]

SetDelayed

:Tag Function in Function[{x,y,z},psi3D[1,1,1,x,y,z]][n_,x_] is Protected.

Out[]=

$Failed

SetDelayed

:Tag Function in Function[{x,y,z},probDensity3D[1,1,1,x,y,z]][n_,x_] is Protected.

Out[]=

$Failed

Function

:Too many parameters in {x,y,z} to be filled from Function[{x,y,z},psi3D[1,1,1,x,y,z]][1,x].

Function

:Too many parameters in {x,y,z} to be filled from Function[{x,y,z},psi3D[1,1,1,x,y,z]][2,x].

Function

:Too many parameters in {x,y,z} to be filled from Function[{x,y,z},psi3D[1,1,1,x,y,z]][3,x].

General

:Further output of Function::fpct will be suppressed during this calculation.

Out[]=

	({x,y,z}psi3D(1,1,1,x,y,z))(1,x)
	({x,y,z}psi3D(1,1,1,x,y,z))(2,x)
	({x,y,z}psi3D(1,1,1,x,y,z))(3,x)
	({x,y,z}psi3D(1,1,1,x,y,z))(4,x)

Function

:Too many parameters in {x,y,z} to be filled from Function[{x,y,z},probDensity3D[1,1,1,x,y,z]][1,x].

Function

:Too many parameters in {x,y,z} to be filled from Function[{x,y,z},probDensity3D[1,1,1,x,y,z]][2,x].

Function

:Too many parameters in {x,y,z} to be filled from Function[{x,y,z},probDensity3D[1,1,1,x,y,z]][3,x].

General

:Further output of Function::fpct will be suppressed during this calculation.

Out[]=

	({x,y,z}probDensity3D(1,1,1,x,y,z))(1,x)
	({x,y,z}probDensity3D(1,1,1,x,y,z))(2,x)
	({x,y,z}probDensity3D(1,1,1,x,y,z))(3,x)
	({x,y,z}probDensity3D(1,1,1,x,y,z))(4,x)

b.EvoluciónTemporaldelaFuncióndeOnda

(*Parámetrosadicionales*)E[n_]:=(n^2Pi^2ħ^2)/(2mL^2)(*Nivelesdeenergía*)(*Funcióndeondadependientedeltiempo*)Psi[n_,x_,t_]:=psi[n,x]Exp[-IE[n]t/ħ](*Graficarlaparterealdelafuncióndeondaendiferentestiempos*)Animate[Plot[Re[Psi[n,x,t]],{x,0,L},PlotRange{-Sqrt[2/L],Sqrt[2/L]},AxesLabel{"x","Re[ψ_n(x,t)]"},PlotLabelStringForm["Función de Onda Real para n=`1`, t=`2`",n,t],PlotStyleThick],{t,0,4mL^2/(Pi^2ħ^2),0.1},AnimationRate1,DefaultDuration10]

Out[]=

t

PlotRe[Psi[n,x,FE`t$$1198073863800479568089080308076254568803]],{x,0,L},PlotRange-

2

L

,

2

L

,

AxesLabel{x,Re[ψ_n(x,t)]},PlotLabelFunción de Onda Real para n=n, t=

FE`t$$1198073863800479568089080308076254568803,PlotStyleThick

2.PozodePotencialInfinitoen2Da.FuncionesdeOndaEstacionariasyDensidadesdeProbabilidad

(*Parámetrosdelpozo*)L=1;(*Longituddelpozoenambasdirecciones*)nMax=2;(*Númeromáximodeestadosencadadirección*)m=1;(*Masadelapartícula*)ħ=1;(*ConstantedePlanckreducida*)(*Definirlafuncióndeondaestacionariaen2D*)psi2D[nx_,ny_,x_,y_]:=Sqrt[4/L^2]Sin[nxPix/L]Sin[nyPiy/L](*Definirladensidaddeprobabilidaden2D*)probDensity2D[nx_,ny_,x_,y_]:=Abs[psi2D[nx,ny,x,y]]^2(*Graficarlafuncióndeondaen2D*)Plot3D[psi2D[1,1,x,y],{x,0,L},{y,0,L},PlotRangeAll,AxesLabel{"x","y","ψ_{1,1}(x,y)"},PlotLabel"Función de Onda Estacionaria 2D para n_x=n_y=1",ColorFunction"Rainbow",MeshNone](*Graficarladensidaddeprobabilidaden2D*)DensityPlot[probDensity2D[1,1,x,y],{x,0,L},{y,0,L},PlotRangeAll,ColorFunction"Rainbow",AxesLabel{"x","y","|ψ_{1,1}(x,y)|^2"},PlotLabel"Densidad de Probabilidad 2D para n_x=n_y=1"]