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## 3. THE QUANTUM MODEL 

In quantization of the theory, we obtain the Wheeler-DeWitt equation 

or 

So, we get a Schr¨ odinger like equation 

where the new variable plays the role of a dynamical time for the theory. Explicitly, the Schr¨ odinger equation can be written as: 

where we have ignored the potential term in this regime. 

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In fact, in quantum cosmology, the Universe is described by a single wave function ψ providing puzzling interpretations when analyzing the differences between ordinary quantum mechanics and quantum cosmology. If we consider the universe wave function as: 

then, by using separation of variables method we obtain 

where l 2 = m 2 + n 2 + k $^{2}$, k 2 = 24 πE ℏ 2 and E , k , m , n and l are arbitrary constants. The solutions to these equations are: 

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