A quantum particle is prepared in the state
|ψ> = 0.8 |E1> + 0.6 i |E2>.
where |E1> and |E2> are energy basis states. A measurement is made of the particle's energy.
What is the probability of measuring the value E2?
A quantum particle is prepared in the state |ψ> = 0.8 |E1> + 0.6 i |E2>....
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of the harmonic oscillator potential corresponding to energies Eo, E1 and E2 (a) Show that the wavefunction is normalised (b) If an observation of energy is made, what is the most likely value of energy and with what probability would it be obtained? (c) If the experiment is...
3.12.2 We perform an experiment in which we prepare a particle in a given quantum mechanical stat e and then measure the momentum of the particle. We repeat this experiment many times and obtain an average result for the momentum (p) (the expectation value of the momennum) For each of the following quantum mechanical states, give the (vector) value of (p) or, if appropriate. (p(t), where ris the time after the preparation of the state. (i) ψ(r)ocexp(ik-r (i) a particle...
Suppose a particle starts out in a linear combination ofjust two stationary states at t = 0: Ψ(x, 0) = c (x) + 2cψ2(x), where the eigen-energies for ψ1 and ψ2 are E1 and E2, respectively. a) Determine c b) What is the expectation value of the energy for the particle? c) What is the wave function Ψ(x, t) at subsequent times?
3. (6 points) Measurements on a two-particle state Consider the state for a system of two spin-1/2 particles, (2]+).I+)2 +1-)[+)2-1-)1-)2). (a) Show that this state is normalized. (b) What is the probability of measuring S: (the z-component of spin for particle 1) to be +h/2? After this measurement is made with this result, what is the state of the system? If we make a measurement in this new state, what is now the probability of measuring S3 = +h/2? (e)...
Consider a system of 1000 particles that can only have two energies, E1 and E2, with E2 > E1. The difference in the energy between these two values IS Δ E2-E1. Assume g1 = g2-1. . Assume ga2- a) Graph the number of particles, nı and n2, in states E1 and E2 as a function of kBT AE, where ks is Boltzmann's constant. Explain your result. b) At what value of kBT /AE do 750 of the particles have the...
Quantum Mechanics question about an infinite square well. A particle in an infinite square well potential has an initial state vector 14() = E1) - %|E2) where E) is the n'th eigenfunctions of the Hamiltonian operator. (a) Find the time evolution of the state vector. (b) Find the expectation value of the position as a function of time.
[20 points] A particle in the simple harmonic oscillator potential with angular frequency a is initially in the ground state: c,y, (x) =Yo(x Att = 0 , the angular frequency of the oscillator suddenly doubles: a} → a½-2.4 The initial wave function can be written in terms of the modified potential (denoted with a tilde:~: Recall that the general form of the first few stationary states for the harmonic oscillator are given on page 56 of your text. a. What...
Consider a system of 1000 particles that can only have two energies, E1 and E2 with E2>E1. The difference in the energy between these two values is delta E= E2-E1. Asume g1=g2=1. a) graph the number of paricle n1, n2 in states of E1 E2 as a function of kbT/deltaE, where kb is Boltzmann constant. Explain the result b) at what value kbT/deltaE do 750 of the particles have the energy E1
This is quantum chemistry. Please explain the answer. Thank you. 4. A hydrogen atom is in a state that is given by (a). Is ψ an eigenfunction of the Hamiltonian for this system? If so, what is the eigenvalue? (b). If a measurement is made of the value of 12 for this system, what are the possible results of the measurement? (c). What is the probability of obtaining each of the results for 12 that you found in (b)? (d)....
please help 1. The eigenfunctions of a particle in a square two-dimensional box with side lengths a = b = L are non, (x, y) = { sin ("T") sin (9,7%) = xn, (x)}n, (y) where n. (c) and on, (y) are one-dimensional particle-in-a-box wave functions in the x and y directions. a. Suppose we prepare the particle in such a way that it has a wave function V (2,y) given by 26,0) = Võru (s. 1) + Vedra ....