Consider a particle of mass m moving under a central potential (spherical symmetry) V(r) = k r where r is the distance of the particle to the center of force and k is a constant. In order to estimate the ground state energy of the system a researcher uses the variational principle with the simple trial function p(r) = e¯ -ar where a is a variational parameter. After a long calculation the researcher finds the following result for the variational integral W[p], that now can be considered a function of the variational parameter a: (hbar)² a² 3k + 2a W(a) 2m What is the best estimate of the ground state energy of the system that can be obtained under this approximation?
Consider a particle of mass m moving under a central potential (spherical symmetry) V(r) = k r where r is the distance of the particle to the center of force and k is a constant. In order to estimate the ground state energy of the system a researcher uses the variational principle with the simple trial function p(r) = e¯ -ar where a is a variational parameter. After a long calculation the researcher finds the following result for the variational integral W[p], that now can be considered a function of the variational parameter a: (hbar)² a² 3k + 2a W(a) 2m What is the best estimate of the ground state energy of the system that can be obtained under this approximation?
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![Consider a particle of mass m moving under a central potential (spherical symmetry)
V(r) = k r
where r is the distance of the particle to the center of force and k is a constant. In order to estimate the ground state energy of the system a researcher
uses the variational principle with the simple trial function
P(r) = e-ar
where a is a variational parameter. After a long calculation the researcher finds the following result for the variational integral W[v], that now can be
considered a function of the variational parameter a:
(hbar)? a?
3k
+
2a
W(a) =
2m
What is the best estimate of the ground state energy of the system that can be obtained under this approximation?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc336536-ba01-4269-8774-733842a8c70d%2F32c546ec-aeee-474c-9a8e-8430ee67d1fa%2Foh6vd4_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a particle of mass m moving under a central potential (spherical symmetry)
V(r) = k r
where r is the distance of the particle to the center of force and k is a constant. In order to estimate the ground state energy of the system a researcher
uses the variational principle with the simple trial function
P(r) = e-ar
where a is a variational parameter. After a long calculation the researcher finds the following result for the variational integral W[v], that now can be
considered a function of the variational parameter a:
(hbar)? a?
3k
+
2a
W(a) =
2m
What is the best estimate of the ground state energy of the system that can be obtained under this approximation?
Transcribed Image Text:(hbar)? r2
W best
а.
2m
Ob.
(hbar)? r2
W best
m
C.
3 k
W pest
2 a
Od.
2/3
3(hbar)?
W best
3km
2m
2(hbar)?
4/3 (hbar k)?/3
1/3
е.
Woen -"
W best
2
m²
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