Expectation values Definition and 122 Threads

I am having some great difficulty getting intuition out of the standard quantization of the Klein-Gordon Lagrangian. consider the H operator. In QM, the expectation values for H in any eigenstates |n> is just <n|H|n> now, in QFT, suppose I have a state |p> in the universe, what do I get if I...

Homework Statement Hi all. Let's say that i have a wave function \Psi (x,t) = A \cdot \exp ( - \lambda \cdot \left| x \right|) \cdot \exp ( - i\omega t) I want to find the expectation value for x. For this I use \left\langle x \right\rangle = \int_{ - \infty }^\infty x \left| \Psi...

The state \Psi = \frac{1}{\sqrt{6}}\Psi-1 + \frac{1}{\sqrt{2}}\Psi1 + \frac{1}{\sqrt{3}}\Psi2 is a linear combination of three orthonormal eigenstates of the operator Ô corresponding to eigenvalues -1, 1, and 2. What is the expectation value of Ô for this state? (A) 2/3 (B)...

i'm just not sure on this little detail, and its keeping me from finishing this problem. take the arbitrary operator \tilde{p}^{n}\tilde{y}^{m} where p is the momentum operator , and x is the x position operator the expectation value is then <\tilde{p}^{n}\tilde{y}^{m} > is this the same...

Homework Statement A particle moves in a sequence of steps of length L. The polar angle \theta for each step is taken from the (normalized) probability density p(\theta). The azimuthal angle is uniformly distributed. Suppose the particle makes N steps. My question is how do I find the...

[SOLVED] Expectation Values of Spin Operators Homework Statement b) Find the expectation values of S_{x}, S_{y}, and S_{z} Homework Equations From part a) X = A \begin{pmatrix}3i \\ 4 \end{pmatrix} Which was found to be: A = \frac{1}{5} S_{x} = \begin{pmatrix}0 & 1 \\ 1 & 0...

For a particle in the state Y(l=3, m=+2), how do I find <Lx^2> + <Ly^2> ? I'm lost. THanks!

Homework Statement How do I get the expectation value of operator \sigma using density matrix \rho in a trace: Tr\left(\sigma\rho\right) I have \sigma and \rho in matrix form but how do I get a number out of the trace?

QM Harmonic Oscillator, expectation values Hello. I am working on a problem involving the 1-dimensional quantum harmonic oscillator with energy eigenstates |n>. The idea of the exercise is to use ladder operators to obtain the results. I feel I am getting a reasonably good hang of this, but my...

I am just starting an introduction to quantum mechanics this semester, and it's hard for me to do some of my homework and follow some of the lectures because I can't grasp the actual 'physical' meaning of some of the concepts. What do they mean by the expectation values? For example...

Very basic question which has confused me: if the variance of an expectation value <A> is: uncertainty of A=<(A-<A>)^2>^0.5 how is this equal to: (<A^2>-<A>^2)^0.5 ??

Homework Statement 6) A particle in the infinite square well has the initial wave function Ψ(x,0)= Ax when 0<=x<=a/2 Ψ(x,0)= A(a-x) when a/2<=x<=a a) Sketch Ψ(x,0), and determine the constant A. b) Find Ψ(x,t) c) Compute <x> and <p> as functions of time. Do they oscillate? With what...

Homework Statement Calculate the expectation values of x, x^2 for a particle in a one dimensional box in state \Psi_n Homework Equations \Psi_n = \sqrt{\frac{2}{a}}sin(\frac{n\pi x}{a}) The Attempt at a Solution i formed the integral \int_{-\infty}^{+\infty}\Psi ^2 x dx as the...

Homework Statement I need to show that a particle in an infinite potential well in the nth energy level, obeys the uncertainty principle and also show which state comes closest to the limit of the uncertainty principle. This means i have to calculate <x>, <x^2>, <p> and <p^2>Homework...

How much sense does it make to compute expectation value of an observable in a limited interval? i.e. \int_a^b \psi^* \hat Q \psi dx. rather than \int_{-\infty}^{\infty} \psi \hat Q \psi dx Apparently, it shouldn't make any sense for it gives weird results when you compute e.v. of momentum for...

Hello, I have a problem that wants me to find the expectation value of <r> <r^2> for the ground state of hydrogen (part a.). My friend and I already completed the exercise but I'm concerned about how we found the expectation value. Since the ground state of hydrogen is only dependent on r do...

I'm given that there is a harmonic oscillator in a state that is a superposition of the ground and first excited stationary states given by \psi = \frac{1}{\sqrt{2}}\abs{\psi_0(x,t) + \psi_1(x,t)}, where \psi_0 = \psi_0(x)e^{\frac{-iE_0t}{\hbar}} and \psi_1 = \psi_1(x)e^{\frac{-iE_1t}{\hbar}}...

Is it true that all expectation values must be real? So if I get an imaginary value, does it mean I made a mistake? Or it doesn't matter and I can just take the absolute value of the expectation? The momentum operator has an 'i' in it. But after doing, Psi*[P]Psi, I have an expression with 'i'...

Two quick ones :) Hi, two questions: 1) How can I find the expectation value of the x-component of the angular momentum, \langle L_x \rangle, when I know \langle L^2 \rangle and \langle L_z \rangle? 2) Say, I have a state |\Psi \rangle and two operators A and B represented as matrices...

Given the wave function: \psi (x,t) = Ae^ {-\lambda \mid x\mid}e^ {-(i ) \omega t} where A, \lambda , and \omega are positive real constants I'm asked to find the expectation values of x and x^2. I know that the values are given by <x> = \int_{-\infty}^{+\infty} x(A^2)e^...

Here is a question that I have found in my quantum text which I have been thinking about for a few days and am unable to make sense of. If there is an operator A whose commutator with the Hamiltonian H is the constant c. [H,A]=c Find <A> at t>0, given that the system is in a normalized...

I am having trouble applying this concept to simple things. Like a die where we let s be the number of spots shown by a die thrown at random. How could I compute the expectation value of s? And how would I compute the mean square deviation. Would the expectation value just be <s>=1/N...