# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sat, 25 May 2013 06:23:25 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 4 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: solution to the TDSE for a certain particle of mass mPosted: Tue, 6 Dec 2011 03:29:26 UTC
 S.O.S. Newbie

Joined: Tue, 6 Dec 2011 03:21:42 UTC
Posts: 2
The solution to the TDSE for a certain particle of mass m is:
*(x,t) = A x exp(-yx + i (hy**/4***m)t) for x>0
=0 for x <****0.
where y is real and postive, h is Planck's constant, and A is a normalization constant.

KEY (sorry I didn't have a greek keyboard):
*=Psi.
**this is squared.
***this is Pi.
****this is less than or equal to.
a). Is wave function odd, even, or neitiher odd nor even (in x)?
b). Show that * is an eigenfunction of energy, and find its energy eigenvalue.
c). Find the expectation value for the particle's position.
d). If Px is the usual 1D momentum operator, find the function that results when Px operates on *(x,t)
e). Find the potential V(x) in which the particle moves.
f). Does the given wave function describe a particle that is bound or unbound?
g). If * describes a bound particle: which energy state is it in (ground, first, excited, etc.)? If * describes an unbound particle, what is the expectation value of the momentum?
h). If * describes a bound particle: consider a beam of light in which each photon has energy equal the binding energy of the particle. Find a formula for the wavelength of the light.
If * describes an unbound particle: Consider a beam of light in which each photon has momentum equal to the particle's expectation value for momentum. Find a formula for the wavelength of the light.

Top

 Post subject: Re: solution to the TDSE for a certain particle of mass mPosted: Tue, 6 Dec 2011 03:36:08 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
dej wrote:
The solution to the TDSE for a certain particle of mass m is:
*(x,t) = A x exp(-yx + i (hy**/4***m)t) for x>0
=0 for x <****0.
where y is real and postive, h is Planck's constant, and A is a normalization constant.

KEY (sorry I didn't have a greek keyboard):
*=Psi.
**this is squared.
***this is Pi.
****this is less than or equal to.
a). Is wave function odd, even, or neitiher odd nor even (in x)?
b). Show that * is an eigenfunction of energy, and find its energy eigenvalue.
c). Find the expectation value for the particle's position.
d). If Px is the usual 1D momentum operator, find the function that results when Px operates on *(x,t)
e). Find the potential V(x) in which the particle moves.
f). Does the given wave function describe a particle that is bound or unbound?
g). If * describes a bound particle: which energy state is it in (ground, first, excited, etc.)? If * describes an unbound particle, what is the expectation value of the momentum?
h). If * describes a bound particle: consider a beam of light in which each photon has energy equal the binding energy of the particle. Find a formula for the wavelength of the light.
If * describes an unbound particle: Consider a beam of light in which each photon has momentum equal to the particle's expectation value for momentum. Find a formula for the wavelength of the light.

That's quite the problem. What have you done on it? We're not here to do that huge amount of work for students, but we are glad to help if you show what you've done and where you are stuck.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: solution to the TDSE for a certain particle of mass mPosted: Tue, 6 Dec 2011 04:56:00 UTC
 S.O.S. Newbie

Joined: Tue, 6 Dec 2011 03:21:42 UTC
Posts: 2
Thank you for your message. This is what I have done so far, but I know it is not correct. Sorry I don't have a greek keyboard.
a). Even, 4 Pi makes it an even valued function.
b). Psi(x,t)= Ax e
E=Psi (x,t) t/dt= -yx + i (hy2/4Pi m x Ax e (-yx +i(hy2/4Pi m)t)
c). expectation value PSI(x,t) probability of Particles location.
Psi (x,t)2 = (Ax e(-yx+i(hy2/4Pi m)t)2
d). Px x Psi (x,t) = A(-y/p +(hy2/4Pi m)t)
e). Psi (x,t) v(x)= Psi (x,t) d/dx
1/2 Ax2 (-yx + i(y2/4Pi m)t) + Ax (i(hy2/4 Pi M )t)

f). bound, time dependence, Psi (x,t)
g). E= Psi(v,t)= Ax (-y +I(y2/4 Pi m)t)
P= Ax (-yx + I (y2/4Pi)t)

h). Lambda = h/Ax (-gamma + i h y2/4Pi) t

Top

 Post subject: Re: solution to the TDSE for a certain particle of mass mPosted: Tue, 6 Dec 2011 05:03:48 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
So for starters, even functions are functions which have the property that when you switch the variable for its opposite you get the same thing, and that's not the case with your function.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 4 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous