Show that in Dirac's equation, matrices have dimensions of 4n, where n= 1, 2, 3...

Expert Solution

genius_generous answered 2 years ago

1. Prove or Disprove: If n is a nonnegative integer, then 5 | (24n + 39n)

1. Prove or Disprove: If n is a nonnegative integer, then 5 | (2*4n + 3*9n)

1. Use the ę notation to prove the following limits: lim n→∞ [n^2+ 3ncos(2n+1)+2] / [n^2−nsin(4n+3)+4]...

1. Use the ę notation to prove the following limits: lim n→∞ [n^2+ 3ncos(2n+1)+2] / [n^2−nsin(4n+3)+4] = 1 2. Let {an} a sequence converging to L > 0. Show ∃N ∈ N, ∀n ∈ N, n ≥ N, an > 0 3.Let {an} a sequence converging to L. Let {bn} a sequence such that ∃Nb ∈ N, ∀n ∈ N, n ≥ Nb, an = bn. Show that {bn} converges to L as well. Thank you. Please complete proofs fully.

Suppose A=(7B^n)/(CD), where A has dimensions [T]/[L]^3, B has dimensions [T], C has dimensions [T][M]^2, and...

Suppose A=(7B^n)/(CD), where A has dimensions [T]/[L]^3, B has dimensions [T], C has dimensions [T][M]^2, and D has dimensions [L]^3/[M]^2. Using dimensional analysis, find the value of the exponent n.

Show that (a)Sn=<(1 2),(1 3),……(1 n)>. (b)Sn=<(1 2),(2 3),……(n-1 n)> (c)Sn=<(1 2),(1 2 …… n-1 n)>

Derive the Dirac gamma matrices for 2-space dimensions and 1-time dimension.

Show that two m×n matrices are equivalent if and only if they have the same invariant...

Show that two m×n matrices are equivalent if and only if they have the same invariant factors, i.e. (by Problem 4), if and only if they have the same Smith normal form.

series from n=1 to infinity of (4n) / [ (3n^3/2) +7n -9]. the answer should include...

series from n=1 to infinity of (4n) / [ (3n^3/2) +7n -9]. the answer should include if its converging or diverging by which method

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this...

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this is indeed the correct limit. (b) Use an epsilon, N argument to show that {1/(n^(1/2))} converges to 0. (c) Let k be a positive integer. Use an epsilon, N argument to show that {a/(n^(1/k))} converges to 0. (d) Show that if {Xn} converges to x, then the sequence {Xn^3} converges to x^3. This has to be an epsilon, N argument [Hint: Use the difference...

1) Solve the Laplace equation ∇^2(u)=0 (two dimensions so ∂^2/∂a^2 + ∂^2/∂b^2) where the boundaries of...

1) Solve the Laplace equation ∇^2(u)=0 (two dimensions so ∂^2/∂a^2 + ∂^2/∂b^2) where the boundaries of the rectangle are 0 < a < m, 0 < b < n with the boundary conditions: u(a,0) = 0 u(a,n) = 0 u(0,b) = 0 u(m,b)= b^2

(a) The n × n matrices A, B, C, and X satisfy the equation AX(B +...

(a) The n × n matrices A, B, C, and X satisfy the equation AX(B + CX) ?1 = C Write an expression for the matrix X in terms of A, B, and C. You may assume invertibility of any matrix when necessary. (b) Suppose D is a 3 × 5 matrix, E is a 5 × c matrix, and F is a 4 × d matrix. Find the values of c and d for which the statement “det(DEF) =...

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