Quantum Physics energy between states

[frozen7]

A 1.5kg mass vibrates at an amplitude of 3cm on the end of a spring of spring constant 20N/m
(a) If the energy of the spring is quantized, find its quantum number.
(b) If n changes by 1, find the fractional change in energy of the spring.

I have solved part (a) but I could not solve part (b)

Does it mean the difference of energy between two continuous quantum?

 

[siddharth]

A 1.5kg mass vibrates at an amplitude of 3cm on the end of a spring of spring constant 20N/m
(a) If the energy of the spring is quantized, find its quantum number.
(b) If n changes by 1, find the fractional change in energy of the spring.
I have solved part (a) but I could not solve part (b)
Does it mean the difference of energy between two continuous quantum?

Yes, it asks for the difference in Energy between the 2 states. The energy difference you get should be very small, as the mass is quite large.

 

[quicknote]

I would like to clarify that energy in quantum physics is not quantized in the same way as, for example, the energy levels of an atom. In quantum mechanics, energy is described by a wave function and can exist in a continuous spectrum of values. Therefore, the concept of a "quantum number" for energy is not applicable in this scenario.

In terms of the given situation, the energy of the spring can be calculated using the formula E = 1/2kx^2, where k is the spring constant and x is the amplitude. Plugging in the values given, we get E = 1/2(20 N/m)(0.03 m)^2 = 0.009 J. This is the total energy of the system and it does not have a specific "quantum number."

As for part (b), if n represents the number of nodes in the wave function, then a change of 1 in n would correspond to a change in the number of energy levels or states of the system. This would result in a change in the energy of the system, but it is not possible to determine the exact fractional change without knowing the specific values of n and the energy levels. In general, a change in n would result in a change in the energy of the system, but the exact magnitude of this change cannot be determined without further information.