Wave function: Quantum Mechanical Hamonic Osculator, n=0, 1, 2, 3.
Prove the following equation is true:
(reduced mass)
Wave function: Quantum Mechanical Hamonic Osculator, n=0, 1, 2, 3. Prove the following equation...
a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x, t) = Acos(kx − t) where A, k, are positive constants. 2. h(x, t) = Ae where A, k, are positive constants. 3. p(x, t) = Asinh(kx − t) where A, k, are positive constants. 4. q(x, t) = Ae where A, a, are positive constants. 5. An arbitrary function: f(x, t) = f(kx−t) where k and are positive constants. (Hint: Be careful with...
Solve the following wave partial differential equation of the
vibration of string for ?(? ,?).
yxx=16ytt
y(0,t)=y(1,t)=0
y(x,0)=2sin(x)+5sin(3x)
yt(x,0)=6sin(4x)+10sin(8x)
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How many orbitals are described by each of the below
combinations of quantum numbers?
n = 3, ℓ =0
orbitals
n = 4, ℓ = 2, mℓ = 2
orbitals
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suppose
prove that 0 is the only eigenvalue of N
(hint: fist show 0 is an eigenvalue of N, and then show if
is any
eigenvalue then =0
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Which of the following sets of quantum numbers contains an
error?
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(a) Find the Fourier transform of the following function (b) Using Fourier transforms, solve the wave equation , -∞<x<∞ t>0 and bounded as ∞ f(r)e We were unable to transcribe this imageu(r, 0)e 4(r.0) =0 , t ur. We were unable to transcribe this image f(r)e u(r, 0)e 4(r.0) =0 , t ur.
Solve the wave equation
a2
∂2u
∂x2
=
∂2u
∂t2
, 0 < x < L, t > 0
(see (1) in Section 12.4) subject to the given conditions.
u(0, t) = 0, u(L, t) = 0
u(x, 0) =
4hx
L
,
0
<
x
<
L
2
4h
1 −
x
L
,
L
2
≤
x
<
L
,
∂u
∂t
t = 0
= 0
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Suppose that
is a bounded function with following Lower and Upper
Integrals:
and
a) Prove that for every
, there exists a partition
of
such that the difference between the upper and lower sums
satisfies
.
b) Furthermore, does there have to be a subdivision such that
. Either prove it or find a counterexample and show to the
contrary.
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Which of the following statements are true? Select all that apply. 1.) For any quantum mechanical problem, the set of eigenfunctions is larger than the set of wave functions. 2.) The set of all wave functions must satisfy the boundary conditions as well as satisfy the conditions that allow us to interpret the square of the magnitude of the wave function in terms of probability. 3.) For any quantum mechanical problem, the set of wave functions is larger than the...
Set Proof:
1. Prove that if S and T are finite sets with |S| = n and |T| =
m, then |S U T| <= (n + m)
2. Prove that finite set S = T if and only if (iff) (S
Tc) U (Sc T) =
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