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The optimized variation wave functions gives:
- a)All properties and energy of same quality
- b)Properties better than the energy
- c)Energy better than properties
- d)Equal kinetic and potential energy values.
Correct answer is option 'A'. Can you explain this answer?
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The optimized variation wave functions gives:a)All properties and ener...
The optimized variation wave functions give all the properties and energy of the same quality. This means that the wave functions provide an accurate description of both the properties and the energy of the system under consideration.
Explanation:
1. Optimized Variation Wave Functions:
- Optimized variation wave functions are mathematical representations of the electronic wave function in a quantum mechanical system. These wave functions are obtained by optimizing the parameters of a given trial wave function to minimize the total energy of the system.
2. Properties and Energy:
- In quantum mechanics, properties such as position, momentum, and energy are described by operators that act on the wave function. The expectation values of these operators can be calculated using the wave function.
3. Quality of Properties and Energy:
- The quality of properties and energy obtained from wave functions refers to how well they describe the actual behavior of the system. A wave function that accurately predicts the properties and energy of a system is considered of high quality.
4. Option A: All Properties and Energy of the Same Quality:
- Option A states that the optimized variation wave functions give all the properties and energy of the same quality. This means that the wave functions provide an accurate description of both the properties and the energy of the system under consideration.
5. Reasoning behind Option A:
- When the parameters of the trial wave function are optimized, the resulting wave function becomes a better approximation to the true wave function of the system. As a result, the expectation values of the operators corresponding to various properties can be calculated more accurately.
- Similarly, by minimizing the total energy of the system, the optimized variation wave functions provide an accurate prediction of the energy.
- Therefore, by optimizing the wave function, we can obtain both the properties and energy of the system with high accuracy.
In conclusion, the optimized variation wave functions provide all the properties and energy of the same quality. By optimizing the parameters of the trial wave function, these wave functions accurately describe the properties and energy of the system under consideration.
Explanation:
1. Optimized Variation Wave Functions:
- Optimized variation wave functions are mathematical representations of the electronic wave function in a quantum mechanical system. These wave functions are obtained by optimizing the parameters of a given trial wave function to minimize the total energy of the system.
2. Properties and Energy:
- In quantum mechanics, properties such as position, momentum, and energy are described by operators that act on the wave function. The expectation values of these operators can be calculated using the wave function.
3. Quality of Properties and Energy:
- The quality of properties and energy obtained from wave functions refers to how well they describe the actual behavior of the system. A wave function that accurately predicts the properties and energy of a system is considered of high quality.
4. Option A: All Properties and Energy of the Same Quality:
- Option A states that the optimized variation wave functions give all the properties and energy of the same quality. This means that the wave functions provide an accurate description of both the properties and the energy of the system under consideration.
5. Reasoning behind Option A:
- When the parameters of the trial wave function are optimized, the resulting wave function becomes a better approximation to the true wave function of the system. As a result, the expectation values of the operators corresponding to various properties can be calculated more accurately.
- Similarly, by minimizing the total energy of the system, the optimized variation wave functions provide an accurate prediction of the energy.
- Therefore, by optimizing the wave function, we can obtain both the properties and energy of the system with high accuracy.
In conclusion, the optimized variation wave functions provide all the properties and energy of the same quality. By optimizing the parameters of the trial wave function, these wave functions accurately describe the properties and energy of the system under consideration.
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The optimized variation wave functions gives:a)All properties and energy of same qualityb)Properties better than the energyc)Energy better than propertiesd)Equal kinetic and potential energy values.Correct answer is option 'A'. Can you explain this answer?
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