Consider a particle of mass m moving in a 2-dimensional rectangular box of sides L„ and Ly, with L. 2Ly. If we use the symbols E, to denote the energy of the ground state of the system, Eel the energy of the first excited state, Ee2 the energy of the second excited state, and Ee3 the energy of the third excited state, what are the numerical values of the ratios Ee1/Eg, Ee2/Eg, and Ee3/E,?
Consider a particle of mass m moving in a 2-dimensional rectangular box of sides L„ and Ly, with L. 2Ly. If we use the symbols E, to denote the energy of the ground state of the system, Eel the energy of the first excited state, Ee2 the energy of the second excited state, and Ee3 the energy of the third excited state, what are the numerical values of the ratios Ee1/Eg, Ee2/Eg, and Ee3/E,?
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Transcribed Image Text:Consider a particle of mass m moving in a 2-dimensional rectangular box of sides
La and Ly, with Le
2Ly. If we use the symbols E, to denote the energy of the
ground state of the system, Ee1 the energy of the first excited state, Ee2 the energy of
the second excited state, and Ee3 the energy of the third excited state, what are the
numerical values of the ratios Ee1/Eg, Ee2/Eg, and Ee3/E,?
Expert Solution
Step 1
Let m denotes the particle mass, Lx and Ly denote the sides of the box, Eg denotes the ground energy, nx and ny denotes the quantum numbers, Ee1, Ee2, and Ee3 denote the 1st, 2nd, and the 3rd excited states. Therefore, the ground state energy can be determined by taking nx and ny equal to 1 as,
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