Infinite square well Definition and 148 Threads

Homework Statement You have a potential well, it's 1-dimensional and has a width of 0 to a. All of a sudden the wall of the well is pushed inward so that it's half as wide. Now the well is only extending from 0 to a/2. in the well is a particle (mass m) that is in the first excited state...

[Note from mentor: this thread originated in a non-homework forum, therefore it doesn't use the standard homework template] ------------------------------------------ This exercise pops up in the Cavendish Quantum Mechanics Primer (M. Warner and A. Cheung) but I can't seem to figure it out. So...

Homework Statement The wording of the question is throwing me off. It is a standard inf. pot. well problem and we are given the initial position of the particle to be in the left fourth of the box, \Psi(x,0)=\sqrt{\frac{4}{a}} We are asked to a) write the expansion of the wave function in...

Homework Statement A particle of mass ##m## is constrained to move between two concentric hard spheres of radii ##r = a## and ##r = b##. There is no potential between the spheres. Find the ground state energy and wave function. Homework Equations $$\frac{-\hbar^2}{2m} \frac{d^2 u}{dr^2} +...

Hi all, So I was recently set straight on the fact that bound state does *not* necessarily mean E<0 but rather is the statement that E<V(+/- infinity). So how do we apply this definition to the infinite square well where the potential at +/- infinity vanishes, and yet the bound states have...

Ok here's a potential I invented and am trying to solve: V = -Vo in -b<x<b and 0 in -a<x<-b , b<x<a where b<a and ∞ everywhere elseI solved it twice and I got the same nonsensical transcendental equation for the allowed energies: \frac{-k}{\sqrt{z_0 - k^2}} \frac{e^{2kb} +...

Homework Statement Homework Equations The Attempt at a Solution I have managed to do the first 3 parts of the questions. The last two 4 markers are the ones I am having difficulties with. I have tried using the expansion postulate which states the wavefunction is equal to the...

Homework Statement Show that the energy levels of a double square well V_{S}(x)= \begin{cases} \infty, & \left|x\right|>b\\ 0, & a<\left|x\right|<b\\ \infty, & \left|x\right|<a \end{cases} are doubly degenerate. (Done) Now suppose that the barrier between -a and a is very high, but finite...

Homework Statement A particle is in a bound state of the infinite square well. It is in a state represented by the following wavefunction, written here at t=0: ψ(x)= -√(2/3)√(2/L) * sin (3πx/L) + i*√(1/3)√(2/L) * sin (2πx/L) (a)Write the full time-dependent wavefunction for this state...

Homework Statement A Particle energy A trapped in infinite square well. U(x)=0 for 0<x<L and U(x)=U0 for L<x<2L. find the wave function of the particle when A) E>U0 B) E<U0 C) E=U0. Homework Equations 1-D time independent Schrodinger equation. The Attempt at a Solution I have...

In finding solutions to the time independent Schrodinger equation we have to normalize \psi to find the constant A. So we get \int_{0}^{a} |A|^{2} sin^{2}(kx) dx = |A|^2 \frac{a}{2}=1 For A we then get |A|^2 = \frac{2}{a} . Griffiths says that this only determines the magnitude of A but...

Homework Statement Normalize: \Psi_1 (x,t) = N_1 \cos(\frac{\pi x}{L}) e^{-\frac{iE_1t}{\hbar}} Where N_1 and E_1 are the normalization constant and energy for the ground state of a particle in an infinite square well. Homework Equations Normalization Condition: \int_\infty^\infty P(x,t)...

Consider the following potential function: V=αδ(x) for x=0 and V=∞ for x>a and x<-a , solve the shroedinger equation for the odd and even solutions. solving the shroedinger equation I get ψ(x)=Asin(kx) +Bcos(kx) for -a<x<0 and ψ(x)=Asin(kx) +Bcos(kx) for 0<x<a is it...

I have been going through my textbook deriving equations in preparation for my test on QM tomorrow. I noticed in the infinite square well that i was unable to complete the normalization. My textbook, Griffiths reads : (integral from 0 to a) ∫|A|^2 * (sin(kx))^2 =|A|^2 * (a/2) =1 Therefore...

Hey guys, this is my first post so go easy on me. I was looking over the simple case of a 1D particle restrained inside an infinite square well potential ("particle in a box") and was having some difficulty understanding the relationship between the energy states and the expectation value for...

Homework Statement Particle in well: V(x)=0 for |x|<\frac{L}{2} V(x)=∞ for |x|>\frac{L}{2} initial wave function \Psi(x,0)=\frac{1}{√L}[cos\frac{\pi*x}{L}+ i*sin\frac{2*\pi*x}{L}] a) calc P(p,t) (momentum prob density) Homework Equations Anything from Griffiths QM The Attempt at a...

Homework Statement A particle, mass m propagates freely in a box, length L. The energy states are: ϕ_n(x) = (2/L)^(1/2)sin(n∏x/L) and energies E_n = n^2∏^2/(2mL^2) at time t=0 the system is in state ϕ_1 and the perturbation V=kx is applied (k constant) and turned off at t=T...

Homework Statement An electron in a one-dimensional infinite square well potential of length L is in a quantum superposition given by ψ = aψ1+bψ2, where ψ1 corresponds to the n = 1 state, ψ2 corresponds to the n = 2 state, and a and b are constants. (a) If a = 1/3, use the normalization...

Suppose you have an electron in the infinite square well. The system is completely isolated from the rest of the world and has been its entire lifetime. Do we then know that the wave function describing the electron is an eigenstate of the Hamiltonian? The question arose because I was given a...

A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.I know the process of...

Homework Statement A cubical box whose sides are length L contains eight electrons. As a multiple of $$\frac{h^2}{2mL^2}$$ what is the energy of the ground state of the eight electrons? Assume the electrons do not interact with each other but do not neglect spin. Homework Equations...

Homework Statement Particle is in an infinite square well of width ##L## on an interval ##-L/2<x<L/2##. The wavefunction which describes the state of this particle is of form: $$\psi = A_0\psi_0(x) + A_1\psi_1(x)$$ where ##A_1=1/2## and where ##\psi_0## and ##\psi_1## are ground and first...

Homework Statement Consider a particle in 1D confined in an infinite square well of width a: $$ V(x) = \begin{cases} 0, & \text{if } 0 \le x \le a \\ \infty, & \text{otherwise} \end{cases} $$ The particle has mass m and at t=0 it is prepared in the state: $$ \Psi (x,t=0) = \begin{cases} A...

Homework Statement A particle in the infinite square well has the initial wave function ## \Psi (x, 0) = Ax(a-x), (0 \le x \le a) ##, for some constant A. Outside the well, of course, ## \Psi = 0 ##. Find ## \Psi (x,t) 2. Homework Equations : Equation [1.0]:## \displaystyle c_n =...

An electron in the ground state of a one-dimensional infinite square well of width 1.10 nm is illuminated with light of wavelength 600 nm. Into which quantum state is the electron excited? ok so I first calculated the engery of the electron in the first ground state of the square well...

Homework Statement Solve for the wavefunctions and energy levels of an infinite square well potential extending between -L<x<L. Hint: It may be worth noting that for a potential symmetric in x, then the observed probability density must also be symmetric in x, i. |ψ(x)|2 = |ψ(-x)|2. Homework...

Homework Statement Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third energy level, E3, to the lowest energy level, E1. Homework Equations E_n = \frac{\left (n_{x}^{2}+n_{y}^{2}+n_{z}^{2} \right) \pi^{2}...

ello everybody, how can I calculate the group velocity of a wave package in an infinite square well? I know only how it can be calculated with a free particle, the derivation of the dispersion relation at the expectation value of the moment. But in the well, there are only discrete...

Please I'm new here, and would need your help with identifying what sort of potential function is described by the following expression: V(x) = 0 for |x| < 1, =1 at x = \pm 1, and =\infty for |x|>1. (Note that: \pm is plus (+) or minus (-) sign). Could it be referred to as the infinite...

Ok...this must sound stupid, because i didn't found answer on the web and on my books...but i am having trouble with the infinite square well. I want to calculate <x>. V(x)=0 for 0<=x<=a <x>=\frac{2}{a}\int^{a}_{0} x \sin^2(\frac{n\pi}{a}x)dx Doing integration by parts i got to...

Homework Statement A particle in an infinite box is in the first excited state (n=2). Obtain the expectation value 1/2<xp+px> 2. The attempt at a solution Honestly, I don't even know where to begin. I assumed V<0, V>L is V=∞ and 0<V<L is V=0 I tried setting up the expectation...

Hi I have attached my attempt of solving the infinite square well for Energy. The value I get is different from that of the book, also in the attachment, Kindly explain if my answer is correct given the fact that I proceeded step by step and used no tricks. Thank you.

Homework Statement An electron is trapped in an infinitely deep potential well 0.300nm in width. (a) If the electron is in its ground state, what is the probability of finding it within 0.100nm of the left-hand wall? (b) Repeat (a) for an electron in the 99th excited state (n=100). (c) Are...

Homework Statement Quantum mechanics is absolutely confusing me. A proton is confined in an infinite square well of length 10-5nm. Calculate the wavelength and energy associated with the photon that is emitted when the proton undergoes a transition from the first excited state (n=2) to the...

Homework Statement An electron is trapped in an infinite square-well potential of width 0.5 nm. If the electron is initially in the n=4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state?Homework Equations ΔE=13.6(1/nf2-1/ni2)...

Hi all, just studying for my final exam and needed a little clarification on this. Our prof did an example: Consider a particle of mass m moving in the nth energy eigenstate of a one-dimensional infinite square well of width L. What is the uncertainty in the particle's energy? He said the...

Schrodinger and Infinite Square Well... hell Homework Statement Show that Schrodinger Equation: \frac{d^{2}\psi(x)}{dx^{2}}+k^{2}\psi(x)=0 has the solution \psi(x)=A\sin(kx) Homework Equations k=\frac{\sqrt{2mE_{tot}-E_{pot}}}{\hbar} The Attempt at a Solution I already know that...

Assume that you have a one dimension box with infinite energy outside, and zero energy from 0 to L. Then my understanding of the Schrodinger equation is that the equation inside will be: -h^2/2m*d2/dx2ψ = ihd/dtψ And the energy eigenstates are given by ψ(x,t) = e-iwt*sin(kx) where k = n*π/L...

Homework Statement We're modelling an ammonia maser with a double infinite square well defined by: V(x) = \begin{cases} V_{0} & |x| < b - \frac{a}{2}\\ 0 & b-\frac{a}{2} < |x| < b+\frac{a}{2}\\ \infty & |x| \geq b + \frac{a}{2} \end{cases} I have had no trouble with the assignment up until...

Homework Statement Find the momentum-space wave function for the nth stationary state of the infinite square well. Homework Equations Nth state position-space wavefunction: \Psi_n(x,t) = \sqrt(\frac{2}{a})sin(\frac{n\pi}{a}x)e^{-iE_nt/\hbar}. Momentum operator in position space: \hat{p} =...

Homework Statement A wavefunction in an infinite square well in the region -L/4≤x≤3L/4 is given by ψ= Asin[(πx/L)+δ] where δ is a constant Find a suitable value for δ (using the boundary conditions on ψ) Homework Equations The Attempt at a Solution Asin[(πx/L)+δ]=?

I have read similar threads about this problem but I wasn't able to make progress using them. Homework Statement Consider an infinite square-well potential of width a, but with the coordinate system shifted so that the infinite potential barriers lie at x=\frac{-a}{2} and x=\frac{a}{2}...

Hi, I'm stuck in this Griffiths' Introduction to QM problem (#2.8) Homework Statement A particle in the infinite square well has the initial wave function \Psi(x,0) = Ax(a-x) Normalize \Psi(x,0) Homework Equations \int_{0}^{a} |\Psi(x)|^2 dx = 1 The Attempt at a Solution...

I've come across an apparent paradox in elementary quantum mechanics, and after a little Googling, haven't found a reference to it. Here goes, The 1-D infinite square well is a classic problem in introductory QM. We find that the position-space eigenfunctions of the Hamiltonian (the "allowed...

Homework Statement suppose you put 5 electrons into an infinite square well. (a) how do the electrons arrange themselves to achieve the lowest total energy? (explain with help of diagram) (b) give an expression for this energy in terms of electron mass, well width L and planks constant The...

I am new to quantum mechanics so I am just trying to get an understanding of the infinite square well. I have been reading a lot of material and I see a lot of times that the barriers of the well say -L/2 and L/2. I know that outside the well to the left is -infinity and to the right is...

Right guys, I want to get this one straight... We have all seen the simple infinite square well a million times. From it, we can get the condition for the k-vector of the electron that k = n.pi / L Now, I also come across all the time that k = 2n.pi / L When do we use which boundary...

Homework Statement An electron is trapped in a 1.00 nm wide rigid box. Determine the probability of finding the electron within 0.15nm of the center of the box (on either side of the center) for a) n = 1 Homework Equations Int[-0.15nm, 0.15nm] psi^2 dx The Attempt at a Solution I...

Homework Statement As part of my homework, I am solving the TISE for the infinite square well model. The potential is zero for |x| =< a and infinite otherwise. Homework Equations The Attempt at a Solution For |x| >= a, the wavefunction is zero. For |x| =< a, there are...

Homework Statement Consider a point particle of mass m contained between two impenetrable walls at +/- 2a. The potential V(x) between the walls is zero. Assume that at time t=0 the state of the particle is described by the wave function \Psi(x) = A\frac{1+cos(\frac{2*\pi*x}{a})}{2} for...