The parity operator P is defined by ˆ Pψ (x) =ψ (−x) for any function ψ(x)....

The parity operator P is defined by

ˆ Pψ (x) =ψ (−x)

for any function ψ(x).

(a) Prove that this parity operator P is Hermitian.

(b) Find its eigenvalues, and also its eigenfunctions (in terms of ψ(x)).

(c) Prove that this parity operator commutes with the Hamiltonian when potential V(x) is an even function.

Expert Solution

genius_generous answered 6 months ago

A probability distribution function P(x) for a random variable X is defined by P(x) = P...

A probability distribution function P(x) for a random variable X is defined by P(x) = P r{X ≤ x}. Suppose that we draw a list of n random variables X1, X2, X3 · · · Xn from a continuous probability distribution function P that is computable in O(1) time. Give an algorithm that sorts these numbers in linear average case time.

f: R[x] to R is the map defined as f(p(x))=p(2) for any polynomial p(x) in R[x]....

f: R[x] to R is the map defined as f(p(x))=p(2) for any polynomial p(x) in R[x]. show that f is 1) a homomorphism 2) Ker(f)=(x-2)R[x] 3) prove that R[x]/Ker(f) is an isomorphism with R. (R in this case is the Reals so R[x]=a0+a1x+a1x^2...anx^n)

1. The probability mass function of a discrete random variable X is defined as p(x) =...

1. The probability mass function of a discrete random variable X is defined as p(x) = ax for x = 1, 2, 4, 8 (p(x) =0 for all other values) then the value of a is? 2. Let X be a discrete random variable with Var(X) =6.0 and E(X2) = 17.00. Then: E(X) = ? 3. If X is a binomial random variable with parameters n and p, i.e. X ~ b(x; n, p), then the expected value of X...

Asume the wave function Ψ(x) = A/(x²+a²) whith x real, A and a constants a) find...

Asume the wave function Ψ(x) = A/(x²+a²) whith x real, A and a constants a) find the normalized wave function Φ(p) un the momentum space associated to Ψ(x) b) use Φ(p) yo compute the expected values for p, p², and σ_p c) verify if this state fulfills the Heisenberg uncertainty principle

A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...

A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms of a. (b) What is the probability to find the particle at x = 0.21a in a small interval of width 0.01a? (c) What is the probability for the particle to be found between x...

A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...

A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are positive real constants. (a) Using the normalization condition, find b in terms of a. (b) What is the probability to find the particle at x = 0.33a in a small interval of width 0.01a? (c) What is the probability for the particle to be found...

A traveling wave along the x-axis is given by the following wave function ψ(x, t) =...

A traveling wave along the x-axis is given by the following wave function ψ(x, t) = 4.5 cos(2.1x - 11.8t + 0.52),where x in meter, t in seconds, and ψ in meters. Find a) the frequency, in hertz b)The wavelength in meters. c) The wave speed, in meters per second. d) The phase constant in radians.

Consider the wave function Ψ = Ae−α|x| Which of the following boundary conditions are satisfied by...

Consider the wave function Ψ = Ae−α|x| Which of the following boundary conditions are satisfied by the wave function? Group of answer choices Ψ approaches zero as x approaches ±∞ Ψ is single valued. Ψ is finite everywhere. None of the boundary conditions are satisfied.

A) If n=570 and ˆ p (p-hat) =0.21, find the margin of error at a 99%...

A) If n=570 and ˆ p (p-hat) =0.21, find the margin of error at a 99% confidence level Give your answer to three decimals B) If n=15, ¯xx¯(x-bar)=30, and s=20, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place. C) You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is...

Recall that the absolute value |x| for a real number x is defined as the function...

Recall that the absolute value |x| for a real number x is defined as the function |x| = x if x ≥ 0 or −x if x < 0. Prove that, for any real numbers x and y, we have (a) | − x| = |x|. (b) |xy| = |x||y|. (c) |x-1| = 1/|x|. Here we assume that x is not equal to 0. (d) −|x| ≤ x ≤ |x|.

Question

The parity operator P is defined by ˆ Pψ (x) =ψ (−x) for any function ψ(x)....

Solutions

Expert Solution

Related Solutions

A probability distribution function P(x) for a random variable X is defined by P(x) = P...

f: R[x] to R is the map defined as f(p(x))=p(2) for any polynomial p(x) in R[x]....

1. The probability mass function of a discrete random variable X is defined as p(x) =...

Asume the wave function Ψ(x) = A/(x²+a²) whith x real, A and a constants a) find...

A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...

A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...

A traveling wave along the x-axis is given by the following wave function ψ(x, t) =...

Consider the wave function Ψ = Ae−α|x| Which of the following boundary conditions are satisfied by...

A) If n=570 and ˆ p (p-hat) =0.21, find the margin of error at a 99%...

Recall that the absolute value |x| for a real number x is defined as the function...