WOLFRAM|DEMONSTRATIONS PROJECT

NMR Signal Processing Lab: Two Spins-1/2

​
Two Coupled Spins-1/2 Sim
update
shift diff, Δ
500
shift sum, σ
0
J
0
T
2
0.1
Free Induction Decay
connect dots
time zoom
left shift
0
broaden/Hz
0
zero fill
1
Frequency Domain Spectrum
connect dots
vertical scale
p
0
0
p
1
0
L
R
absorption/dispersion
Free Induction Decay
Frequency Spectrum
​This is a Demonstration of signal processing in Fourier-transform nuclear magnetic resonance (NMR) spectroscopy. The time-domain, free induction decay signal for two coupled spins-1/2 is plotted in red. The Fourier transform frequency domain spectrum is shown in blue. The spin Hamiltonian is given by
H=
1
2
(σ+Δ)
I
z
1
+
1
2
(σ-Δ)
I
z
2
+J
I
1
·
I
2
, where the sum and difference of the chemical shifts are given by
σ
and
Δ
, respectively, and
J
is the scalar coupling constant (all in Hertz). Zero and first-order phasing of the spectrum are controlled by
p
0
and
p
1
.